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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2016-06-09</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001290149</issuerCik>
        <issuerName>ProNAi Therapeutics Inc</issuerName>
        <issuerTradingSymbol>DNAI</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001301173</rptOwnerCik>
            <rptOwnerName>Cooper Jeffrey H</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O PRONAI THERAPEUTICS, INC.</rptOwnerStreet1>
            <rptOwnerStreet2>2150 885 WEST GEORGIA ST</rptOwnerStreet2>
            <rptOwnerCity>VANCOUVER</rptOwnerCity>
            <rptOwnerState>A1</rptOwnerState>
            <rptOwnerZipCode>V6C 3E8</rptOwnerZipCode>
            <rptOwnerStateDescription>BRITISH COLUMBIA, CANADA</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>2.06</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2016-06-09</value>
                <footnoteId id="F1"/>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>77670</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F2"/>
            </exerciseDate>
            <expirationDate>
                <value>2026-06-09</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>77670</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>77670</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">Stock options were granted in connection with the reporting person's appointment to the issuer's board of directors on March 18, 2016, such grant date to be effective upon the first trading day on which the issuer was not in a trading black-out period under the issuer's insider trading policy, which was June 9, 2016.</footnote>
        <footnote id="F2">The option vests as to 8.333% of the total shares monthly, beginning on July 9, 2016, with 100% of the total shares vested and exercisable on June 9, 2017, subject to the reporting person's provision of service to the issuer on each vesting date.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Sukhi Jagpal as attorney-in-fact for Jeffrey Cooper</signatureName>
        <signatureDate>2016-06-13</signatureDate>
    </ownerSignature>
</ownershipDocument>
