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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2019-08-06</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001377121</issuerCik>
        <issuerName>Protagonist Therapeutics, Inc</issuerName>
        <issuerTradingSymbol>PTGX</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001120477</rptOwnerCik>
            <rptOwnerName>PATEL DINESH V PH D</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O PROTAGONIST THERAPEUTICS, INC.</rptOwnerStreet1>
            <rptOwnerStreet2>7707 GATEWAY BLVD., SUITE 140</rptOwnerStreet2>
            <rptOwnerCity>NEWARK</rptOwnerCity>
            <rptOwnerState>CA</rptOwnerState>
            <rptOwnerZipCode>94560</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>President and CEO</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2019-08-06</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>10792</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>8.8524</value>
                    <footnoteId id="F2"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>374792</value>
                    <footnoteId id="F3"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">The sales reported on this Form 4 represent shares required to be sold by the Reporting Person to cover tax withholding obligations in connection with the vesting of Restricted Stock Units. These sales are mandated by the Issuer's election under its equity incentive plans to require the satisfaction of tax withholding obligations to be funded by a &quot;sell to cover&quot; transaction and do not represent discretionary trades by the Reporting Person.</footnote>
        <footnote id="F2">The price reported in Column 4 is a weighted average price. These shares were sold in multiple transactions at prices ranging from $8.80 to $9.2504, inclusive. The Reporting Person undertakes to provide to the Issuer, any security holder of the Issuer, or the staff of the Securities and Exchange Commission, upon request, full information regarding the number of shares sold at each separate price within the range.</footnote>
        <footnote id="F3">Includes 1,753 shares acquired by the Reporting Person under the Issuer's 2016 Employee Stock Purchase Plan on March 8, 2019.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Donald A. Kalkofen, Attorney-in-Fact for Dinesh V. Patel, Ph.D.</signatureName>
        <signatureDate>2019-08-08</signatureDate>
    </ownerSignature>
</ownershipDocument>
