<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2017-08-02</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001689813</issuerCik>
        <issuerName>Biohaven Pharmaceutical Holding Co Ltd.</issuerName>
        <issuerTradingSymbol>BHVN</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001226675</rptOwnerCik>
            <rptOwnerName>GREGORY JULIA P</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O BIOHAVEN PHARMACEUTICALS, INC.</rptOwnerStreet1>
            <rptOwnerStreet2>234 CHURCH STREET</rptOwnerStreet2>
            <rptOwnerCity>NEW HAVEN</rptOwnerCity>
            <rptOwnerState>CT</rptOwnerState>
            <rptOwnerZipCode>06510</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Stock Option (right to buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>23.63</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2017-08-02</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>36000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F1"/>
            </exerciseDate>
            <expirationDate>
                <value>2027-08-01</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Shares</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>36000</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>36000</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">This option grant was made pursuant to the issuer's non-employee director compensation policy. The common shares underlying this option vest in three equal installments on August 2, 2018, 2019 and 2020, subject to the reporting person's continuous service with the issuer at each vesting date.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Darren K. DeStefano, Attorney-in-fact</signatureName>
        <signatureDate>2017-08-04</signatureDate>
    </ownerSignature>
</ownershipDocument>
