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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2018-04-26</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001403708</issuerCik>
        <issuerName>Evoke Pharma Inc</issuerName>
        <issuerTradingSymbol>EVOK</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001592848</rptOwnerCik>
            <rptOwnerName>CARLSON MARILYN R.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O EVOKE PHARMA, INC.</rptOwnerStreet1>
            <rptOwnerStreet2>420 STEVENS AVENUE, SUITE 370</rptOwnerStreet2>
            <rptOwnerCity>SOLANA BEACH</rptOwnerCity>
            <rptOwnerState>CA</rptOwnerState>
            <rptOwnerZipCode>92075</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>Chief Medical Officer</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Stock Option (Right to Buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>2.43</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2018-04-26</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>125000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F1"/>
            </exerciseDate>
            <expirationDate>
                <value>2028-02-06</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>125000</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>125000</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">The option grant date was February 7, 2018, subject to approval of the Issuer's Amended and Restated 2013 Equity Incentive Plan (the &quot;Plan&quot;) by the Issuer's stockholders which occurred at the Issuer's annual stockholder meeting on April 26, 2018.  The total number of shares of common stock subject to the option vests in 48 equal monthly installments over the four-year period beginning on January 1, 2018, subject to the reporting person's continued service to the Issuer through each such vesting date. Notwithstanding the foregoing vesting schedule, in no event may the option be exercised prior to the earlier of (i) the date on which the Issuer receives marketing approval from the U.S. Food and Drug Administration of Gimoti, (ii) the second anniversary of the date of grant, or (iii) the date of a &quot;change in control&quot; under Section 2.9 of the Plan.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Matthew J. D'Onofrio, Attorney-in-fact for Marilyn R. Carlson</signatureName>
        <signatureDate>2018-04-27</signatureDate>
    </ownerSignature>
</ownershipDocument>
