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

<!--XBRL Document Created with the Workiva Platform-->
<!--Copyright 2026 Workiva-->
<!--r:019dbaf7-7de9-7ea7-8eae-d5043f4e29c9,g:ec3923a7-ecf4-4d59-aeeb-557827f5035c-->
<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-20260428.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_019dbaf7-7de9-7bd1-afdc-9d04e81a203c" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_CoverAbstract"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentType_019dbaf7-7de9-7940-814c-aaea7ac778ea" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_DocumentType"/>
    <link:presentationArc order="1" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_019dbaf7-7de9-7bd1-afdc-9d04e81a203c" xlink:to="loc_dei_DocumentType_019dbaf7-7de9-7940-814c-aaea7ac778ea" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityRegistrantName_019dbaf7-7de9-73ea-89bf-659f5ab85ec9" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityRegistrantName"/>
    <link:presentationArc order="2" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_019dbaf7-7de9-7bd1-afdc-9d04e81a203c" xlink:to="loc_dei_EntityRegistrantName_019dbaf7-7de9-73ea-89bf-659f5ab85ec9" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentPeriodEndDate_019dbaf7-7de9-71e1-9d56-61e54de95189" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_DocumentPeriodEndDate"/>
    <link:presentationArc order="3" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_019dbaf7-7de9-7bd1-afdc-9d04e81a203c" xlink:to="loc_dei_DocumentPeriodEndDate_019dbaf7-7de9-71e1-9d56-61e54de95189" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityIncorporationStateCountryCode_019dbaf7-7de9-79ca-bc45-b354b8c08213" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityIncorporationStateCountryCode"/>
    <link:presentationArc order="4" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_019dbaf7-7de9-7bd1-afdc-9d04e81a203c" xlink:to="loc_dei_EntityIncorporationStateCountryCode_019dbaf7-7de9-79ca-bc45-b354b8c08213" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityFileNumber_019dbaf7-7de9-749b-a256-a20d0a5a1da0" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityFileNumber"/>
    <link:presentationArc order="5" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_019dbaf7-7de9-7bd1-afdc-9d04e81a203c" xlink:to="loc_dei_EntityFileNumber_019dbaf7-7de9-749b-a256-a20d0a5a1da0" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressAddressLine1_019dbaf7-7de9-7055-a82c-773411bf913b" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityAddressAddressLine1"/>
    <link:presentationArc order="6" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_019dbaf7-7de9-7bd1-afdc-9d04e81a203c" xlink:to="loc_dei_EntityAddressAddressLine1_019dbaf7-7de9-7055-a82c-773411bf913b" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressAddressLine2_019dbaf7-7de9-7cd8-af28-e79a5ad39294" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityAddressAddressLine2"/>
    <link:presentationArc order="7" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_019dbaf7-7de9-7bd1-afdc-9d04e81a203c" xlink:to="loc_dei_EntityAddressAddressLine2_019dbaf7-7de9-7cd8-af28-e79a5ad39294" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressCityOrTown_019dbaf7-7de9-7401-a5b7-cae1cd81bf97" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityAddressCityOrTown"/>
    <link:presentationArc order="8" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_019dbaf7-7de9-7bd1-afdc-9d04e81a203c" xlink:to="loc_dei_EntityAddressCityOrTown_019dbaf7-7de9-7401-a5b7-cae1cd81bf97" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressStateOrProvince_019dbaf7-7de9-7cf6-a2b4-45e5a21ad822" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityAddressStateOrProvince"/>
    <link:presentationArc order="9" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_019dbaf7-7de9-7bd1-afdc-9d04e81a203c" xlink:to="loc_dei_EntityAddressStateOrProvince_019dbaf7-7de9-7cf6-a2b4-45e5a21ad822" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressPostalZipCode_019dbaf7-7de9-7049-91ad-854a57f6504e" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityAddressPostalZipCode"/>
    <link:presentationArc order="10" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_019dbaf7-7de9-7bd1-afdc-9d04e81a203c" xlink:to="loc_dei_EntityAddressPostalZipCode_019dbaf7-7de9-7049-91ad-854a57f6504e" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_CityAreaCode_019dbaf7-7de9-7d53-abed-d971d8d5d6db" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_CityAreaCode"/>
    <link:presentationArc order="11" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_019dbaf7-7de9-7bd1-afdc-9d04e81a203c" xlink:to="loc_dei_CityAreaCode_019dbaf7-7de9-7d53-abed-d971d8d5d6db" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_LocalPhoneNumber_019dbaf7-7de9-7730-987f-c4479b84f67c" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_LocalPhoneNumber"/>
    <link:presentationArc order="12" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_019dbaf7-7de9-7bd1-afdc-9d04e81a203c" xlink:to="loc_dei_LocalPhoneNumber_019dbaf7-7de9-7730-987f-c4479b84f67c" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_WrittenCommunications_019dbaf7-7de9-755f-8d2d-e9ae61c70e7b" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_WrittenCommunications"/>
    <link:presentationArc order="13" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_019dbaf7-7de9-7bd1-afdc-9d04e81a203c" xlink:to="loc_dei_WrittenCommunications_019dbaf7-7de9-755f-8d2d-e9ae61c70e7b" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_SolicitingMaterial_019dbaf7-7de9-7500-bc67-3538ff24fa65" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_SolicitingMaterial"/>
    <link:presentationArc order="14" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_019dbaf7-7de9-7bd1-afdc-9d04e81a203c" xlink:to="loc_dei_SolicitingMaterial_019dbaf7-7de9-7500-bc67-3538ff24fa65" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_PreCommencementTenderOffer_019dbaf7-7de9-765c-bcae-b9b6eacd670c" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_PreCommencementTenderOffer"/>
    <link:presentationArc order="15" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_019dbaf7-7de9-7bd1-afdc-9d04e81a203c" xlink:to="loc_dei_PreCommencementTenderOffer_019dbaf7-7de9-765c-bcae-b9b6eacd670c" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_PreCommencementIssuerTenderOffer_019dbaf7-7de9-75e4-9fdb-90ce28c0f682" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_PreCommencementIssuerTenderOffer"/>
    <link:presentationArc order="16" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_019dbaf7-7de9-7bd1-afdc-9d04e81a203c" xlink:to="loc_dei_PreCommencementIssuerTenderOffer_019dbaf7-7de9-75e4-9fdb-90ce28c0f682" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_Security12bTitle_019dbaf7-7de9-773a-819d-1a072b83453c" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_Security12bTitle"/>
    <link:presentationArc order="17" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_019dbaf7-7de9-7bd1-afdc-9d04e81a203c" xlink:to="loc_dei_Security12bTitle_019dbaf7-7de9-773a-819d-1a072b83453c" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_TradingSymbol_019dbaf7-7de9-77e3-be19-0bfb56b8cdc5" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_TradingSymbol"/>
    <link:presentationArc order="18" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_019dbaf7-7de9-7bd1-afdc-9d04e81a203c" xlink:to="loc_dei_TradingSymbol_019dbaf7-7de9-77e3-be19-0bfb56b8cdc5" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_SecurityExchangeName_019dbaf7-7de9-742b-b577-8a953a8a73fb" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_SecurityExchangeName"/>
    <link:presentationArc order="19" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_019dbaf7-7de9-7bd1-afdc-9d04e81a203c" xlink:to="loc_dei_SecurityExchangeName_019dbaf7-7de9-742b-b577-8a953a8a73fb" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityEmergingGrowthCompany_019dbaf7-7de9-7a17-8c9a-6c549a785e43" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityEmergingGrowthCompany"/>
    <link:presentationArc order="20" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_019dbaf7-7de9-7bd1-afdc-9d04e81a203c" xlink:to="loc_dei_EntityEmergingGrowthCompany_019dbaf7-7de9-7a17-8c9a-6c549a785e43" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityCentralIndexKey_019dbaf7-7de9-78fa-a206-d79392181ff9" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityCentralIndexKey"/>
    <link:presentationArc order="21" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_019dbaf7-7de9-7bd1-afdc-9d04e81a203c" xlink:to="loc_dei_EntityCentralIndexKey_019dbaf7-7de9-78fa-a206-d79392181ff9" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_AmendmentFlag_019dbaf7-7de9-7ae6-a565-8c692b76bd20" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_AmendmentFlag"/>
    <link:presentationArc order="22" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_019dbaf7-7de9-7bd1-afdc-9d04e81a203c" xlink:to="loc_dei_AmendmentFlag_019dbaf7-7de9-7ae6-a565-8c692b76bd20" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
  </link:presentationLink>
</link:linkbase>
