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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2016-05-13</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001305641</rptOwnerCik>
            <rptOwnerName>Parfet Donald R</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>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>Chairman of the Board</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2016-05-13</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>J</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>3204</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>377379</value>
                    <footnoteId id="F2"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Donald R. Parfet 2006 Trust, Dated May 1, 2006</value>
                    <footnoteId id="F3"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>72250</value>
                    <footnoteId id="F4"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>238419</value>
                    <footnoteId id="F5"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Ann VanDeWater Parfet 2006 Revocable Trust, Dated May 5, 2006</value>
                    <footnoteId id="F6"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>4970</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By wife</value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>589</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Apjohn Group, LLC</value>
                    <footnoteId id="F7"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">Represents shares of the issuer's common stock received in connection with a pro rata distribution of shares held by Sigvion Fund I to its limited partners.</footnote>
        <footnote id="F2">Includes (a) 13,605 shares of the issuer's common stock received as a liquidating distribution from Palmero Group LLC (&quot;Palmero&quot;) and (b) 6,768 shares of the issuer's common stock received as a liquidating distribution from Apjohn Ventures Fund, LP (&quot;AVF&quot;).  In prior reports, the reporting person reported beneficial ownership of all of the issuer's securities previously held by each of Palmero and AVF.  As of March 7, 2016, the reporting person no longer had any voting or dispositive control over the issuer's securities held by AVF.  In addition, in connection with the liquidating distribution, Palmero does not currently hold any of the issuer's securities.</footnote>
        <footnote id="F3">The reporting person is the trustee of the Donald R. Parfet 2006 Trust, Dated May 1, 2006.</footnote>
        <footnote id="F4">Includes an aggregate of 2,402 shares of the issuer's common stock received as liquidating distributions from Apjohn Ventures, LLC (&quot;AVLLC&quot;).  AVLLC received shares of the issuer's common stock in connection with liquidating distributions from AVF and Apjohn Ventures Annex Fund LP (&quot;AVAF&quot;).  In prior reports, the reporting person reported beneficial ownership of all of the issuer's securities previously held by each of AVF and AVAF.  As of March 7, 2016, the reporting person no longer had any voting or dispositive control over the issuer's securities held by AVF and AVAF.</footnote>
        <footnote id="F5">Includes 20,516 shares of the issuer's common stock received as a liquidating distribution from Palmero.</footnote>
        <footnote id="F6">The reporting person's wife is the trustee of the Ann VanDeWater Parfet 2006 Revocable Trust, Dated May 5, 2006.  The reporting person disclaims beneficial ownership of such securities, and the inclusion of these securities in this report shall not be deemed an admission of beneficial ownership of the reported securities for purposes of Section 16 or for any other purposes.</footnote>
        <footnote id="F7">The reporting person is the managing member of Apjohn Group, LLC, and has sole voting and dispositive power over the shares held by Apjohn Group, LLC.  The reporting person disclaims beneficial ownership over such securities except to the extent of his pecuniary interest therein, and the inclusion of these securities in this report shall not be deemed an admission of beneficial ownership of the reported securities for purposes of Section 16 or for any other purposes.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Sukhi Jagpal as attorney-in-fact for Donald Parfet</signatureName>
        <signatureDate>2016-05-17</signatureDate>
    </ownerSignature>
</ownershipDocument>
