<?xml version="1.0" encoding="UTF-8"?>

<!--XBRL Document Created with the Workiva Platform-->
<!--Copyright 2024 Workiva-->
<!--r:ae960bf8-ef21-4155-ab62-f7e8d0205249,g:ec670c32-6983-4ce1-8eda-9ea06b6e8ccd-->
<link:linkbase xmlns:link="http://www.xbrl.org/2003/linkbase" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://www.xbrl.org/2003/linkbase http://www.xbrl.org/2003/xbrl-linkbase-2003-12-31.xsd">
  <link:roleRef roleURI="http://www.biohavenpharma.com/role/Cover" xlink:type="simple" xlink:href="bhvn-20240312.xsd#Cover"/>
  <link:presentationLink xlink:role="http://www.biohavenpharma.com/role/Cover" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_dei_CoverAbstract_14192056-4422-42bc-b28d-840e5fe471a0" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_CoverAbstract"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentType_4339e288-e5c6-4bfb-8ed1-d0a98c718a86" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_DocumentType"/>
    <link:presentationArc order="1" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_14192056-4422-42bc-b28d-840e5fe471a0" xlink:to="loc_dei_DocumentType_4339e288-e5c6-4bfb-8ed1-d0a98c718a86" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityRegistrantName_08af5df2-5579-4289-bfb2-d0a73aca89dd" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_EntityRegistrantName"/>
    <link:presentationArc order="2" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_14192056-4422-42bc-b28d-840e5fe471a0" xlink:to="loc_dei_EntityRegistrantName_08af5df2-5579-4289-bfb2-d0a73aca89dd" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentPeriodEndDate_4af018f8-1103-4b38-96a8-240de3912742" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_DocumentPeriodEndDate"/>
    <link:presentationArc order="3" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_14192056-4422-42bc-b28d-840e5fe471a0" xlink:to="loc_dei_DocumentPeriodEndDate_4af018f8-1103-4b38-96a8-240de3912742" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityIncorporationStateCountryCode_cba9af8d-a27d-4c26-8a53-e4e0736d22fc" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_EntityIncorporationStateCountryCode"/>
    <link:presentationArc order="4" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_14192056-4422-42bc-b28d-840e5fe471a0" xlink:to="loc_dei_EntityIncorporationStateCountryCode_cba9af8d-a27d-4c26-8a53-e4e0736d22fc" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityFileNumber_dd3ff7dc-6f27-4179-b0e4-fd7101d98869" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_EntityFileNumber"/>
    <link:presentationArc order="5" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_14192056-4422-42bc-b28d-840e5fe471a0" xlink:to="loc_dei_EntityFileNumber_dd3ff7dc-6f27-4179-b0e4-fd7101d98869" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressAddressLine1_d36bc575-c41b-4b28-9370-20a461624b05" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_EntityAddressAddressLine1"/>
    <link:presentationArc order="6" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_14192056-4422-42bc-b28d-840e5fe471a0" xlink:to="loc_dei_EntityAddressAddressLine1_d36bc575-c41b-4b28-9370-20a461624b05" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressAddressLine2_1e5a736f-f5da-48f1-b84d-063f4c80c494" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_EntityAddressAddressLine2"/>
    <link:presentationArc order="7" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_14192056-4422-42bc-b28d-840e5fe471a0" xlink:to="loc_dei_EntityAddressAddressLine2_1e5a736f-f5da-48f1-b84d-063f4c80c494" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressCityOrTown_77503c10-4d74-421d-add6-cef90de58368" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_EntityAddressCityOrTown"/>
    <link:presentationArc order="8" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_14192056-4422-42bc-b28d-840e5fe471a0" xlink:to="loc_dei_EntityAddressCityOrTown_77503c10-4d74-421d-add6-cef90de58368" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressStateOrProvince_d035454f-069c-4a0a-a229-8c338d7ba96d" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_EntityAddressStateOrProvince"/>
    <link:presentationArc order="9" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_14192056-4422-42bc-b28d-840e5fe471a0" xlink:to="loc_dei_EntityAddressStateOrProvince_d035454f-069c-4a0a-a229-8c338d7ba96d" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressPostalZipCode_40c441ed-bffb-44ae-bbf6-a93614e2099b" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_EntityAddressPostalZipCode"/>
    <link:presentationArc order="10" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_14192056-4422-42bc-b28d-840e5fe471a0" xlink:to="loc_dei_EntityAddressPostalZipCode_40c441ed-bffb-44ae-bbf6-a93614e2099b" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_CityAreaCode_18df1000-05e6-406c-a913-967b0f8d244a" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_CityAreaCode"/>
    <link:presentationArc order="11" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_14192056-4422-42bc-b28d-840e5fe471a0" xlink:to="loc_dei_CityAreaCode_18df1000-05e6-406c-a913-967b0f8d244a" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_LocalPhoneNumber_e033049c-f969-4508-83a2-a6e183d14c25" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_LocalPhoneNumber"/>
    <link:presentationArc order="12" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_14192056-4422-42bc-b28d-840e5fe471a0" xlink:to="loc_dei_LocalPhoneNumber_e033049c-f969-4508-83a2-a6e183d14c25" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_WrittenCommunications_950312d7-df2f-4468-b0e8-d259ed81f83c" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_WrittenCommunications"/>
    <link:presentationArc order="13" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_14192056-4422-42bc-b28d-840e5fe471a0" xlink:to="loc_dei_WrittenCommunications_950312d7-df2f-4468-b0e8-d259ed81f83c" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_SolicitingMaterial_4c347e31-8ecb-4d6e-8878-0d0093ce8951" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_SolicitingMaterial"/>
    <link:presentationArc order="14" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_14192056-4422-42bc-b28d-840e5fe471a0" xlink:to="loc_dei_SolicitingMaterial_4c347e31-8ecb-4d6e-8878-0d0093ce8951" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_PreCommencementTenderOffer_9b1a8d3e-b29b-44d9-bd85-4cf5575e7dc5" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_PreCommencementTenderOffer"/>
    <link:presentationArc order="15" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_14192056-4422-42bc-b28d-840e5fe471a0" xlink:to="loc_dei_PreCommencementTenderOffer_9b1a8d3e-b29b-44d9-bd85-4cf5575e7dc5" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_PreCommencementIssuerTenderOffer_bab429c8-3cd7-43f3-b158-7aafe7266c61" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_PreCommencementIssuerTenderOffer"/>
    <link:presentationArc order="16" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_14192056-4422-42bc-b28d-840e5fe471a0" xlink:to="loc_dei_PreCommencementIssuerTenderOffer_bab429c8-3cd7-43f3-b158-7aafe7266c61" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_Security12bTitle_ac1b92d5-5bfd-42bd-879d-6afb2d612f9f" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_Security12bTitle"/>
    <link:presentationArc order="17" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_14192056-4422-42bc-b28d-840e5fe471a0" xlink:to="loc_dei_Security12bTitle_ac1b92d5-5bfd-42bd-879d-6afb2d612f9f" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_TradingSymbol_135bf46e-9833-44fd-a1b0-397ec6fd9633" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_TradingSymbol"/>
    <link:presentationArc order="18" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_14192056-4422-42bc-b28d-840e5fe471a0" xlink:to="loc_dei_TradingSymbol_135bf46e-9833-44fd-a1b0-397ec6fd9633" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_SecurityExchangeName_70ec93ea-c702-46d5-a23c-ddc604525864" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_SecurityExchangeName"/>
    <link:presentationArc order="19" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_14192056-4422-42bc-b28d-840e5fe471a0" xlink:to="loc_dei_SecurityExchangeName_70ec93ea-c702-46d5-a23c-ddc604525864" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityEmergingGrowthCompany_12e10948-7dc0-4c29-90f3-ac21f66bfbc5" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_EntityEmergingGrowthCompany"/>
    <link:presentationArc order="20" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_14192056-4422-42bc-b28d-840e5fe471a0" xlink:to="loc_dei_EntityEmergingGrowthCompany_12e10948-7dc0-4c29-90f3-ac21f66bfbc5" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityCentralIndexKey_e7b5a556-b7ab-4379-b393-1600c7446cc6" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_EntityCentralIndexKey"/>
    <link:presentationArc order="21" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_14192056-4422-42bc-b28d-840e5fe471a0" xlink:to="loc_dei_EntityCentralIndexKey_e7b5a556-b7ab-4379-b393-1600c7446cc6" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_AmendmentFlag_252d324e-9d1f-4d6d-9be2-863cb65c4149" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_AmendmentFlag"/>
    <link:presentationArc order="22" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_14192056-4422-42bc-b28d-840e5fe471a0" xlink:to="loc_dei_AmendmentFlag_252d324e-9d1f-4d6d-9be2-863cb65c4149" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
  </link:presentationLink>
</link:linkbase>
