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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2020-05-08</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0000884713</issuerCik>
        <issuerName>Primo Water Corp /CN/</issuerName>
        <issuerTradingSymbol>PRMW</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001287961</rptOwnerCik>
            <rptOwnerName>FOWDEN JEREMY S G</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O PRIMO WATER CORPORATION</rptOwnerStreet1>
            <rptOwnerStreet2>4221 WEST BOY SCOUT BOULEVARD</rptOwnerStreet2>
            <rptOwnerCity>TAMPA</rptOwnerCity>
            <rptOwnerState>FL</rptOwnerState>
            <rptOwnerZipCode>33607</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Shares</value>
            </securityTitle>
            <transactionDate>
                <value>2020-05-08</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>10610</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>11.31</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1277830</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Shares</value>
            </securityTitle>
            <transactionDate>
                <value>2020-05-08</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>1349</value>
                    <footnoteId id="F2"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>8.77</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1279179</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">Common Shares were issued pursuant to the Amended and Restated Primo Water Corporation Equity Incentive Plan (the &quot;Plan&quot;) in payment of the reporting person's annual director fee. The number of shares was calculated by dividing $120,000 (the cash amount of the annual director fee) by $11.31 (the closing price of the Common Shares on the New York Stock Exchange on May 8, 2020).</footnote>
        <footnote id="F2">Additional Common Shares were issued pursuant to the Plan in payment of the reporting person's annual director fee for services rendered to the Board of Directors from March 29, 2020, the date the reporting person transitioned from Executive Chairman to Chairman of the Board of Directors, to May 5, 2020, the date of the 2020 Annual Meeting of Shareowners. The number of shares was calculated by pro-rating $120,000 (the cash amount of the annual director fee) for the period of service and dividing the resulting figure by $8.77 (the closing price of the Common Shares on the New York Stock Exchange on March 27, 2020).</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Marni Morgan Poe, Attorney-in-Fact</signatureName>
        <signatureDate>2020-05-12</signatureDate>
    </ownerSignature>
</ownershipDocument>
