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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2016-12-12</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001365101</issuerCik>
        <issuerName>Primo Water Corp</issuerName>
        <issuerTradingSymbol>PRMW</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001230730</rptOwnerCik>
            <rptOwnerName>NORRIS CHARLES A</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>101 NORTH CHERRY STREET</rptOwnerStreet1>
            <rptOwnerStreet2>SUITE 501</rptOwnerStreet2>
            <rptOwnerCity>WINSTON-SALEM</rptOwnerCity>
            <rptOwnerState>NC</rptOwnerState>
            <rptOwnerZipCode>27101</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2016-12-12</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>163274</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>163274</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2016-12-12</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>274045</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F2"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>274045</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>Held in Norris Trust dtd 06/18/02</value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Warrant (right to buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>11.88</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2016-12-12</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>275170</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F3"/>
            </exerciseDate>
            <expirationDate>
                <value>2021-12-12</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>275170</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>275170</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">Mr. Norris acquired 163,274 shares of Primo Water Corporation's (&quot;Primo&quot;) common stock in connection with the acquisition of Glacier Water Services, Inc. (&quot;Glacier&quot;) by Primo on December 12, 2016 (the &quot;Merger&quot;). For each share of Glacier common stock, Mr. Norris received approximately $12.18 in cash, 0.87 of a share of Primo common stock, and a warrant to purchase 0.55 of a share of Primo common stock.  Pursuant to the Agreement and Plan of Merger (the &quot;Merger Agreement&quot;) entered into on October 9, 2016, 115,924 of such shares of Primo common stock received by Mr. Norris were deposited into escrow and are subject to forfeiture during the one-year period ending on December 12, 2017 to satisfy claims with respect to breaches, violations or non-fulfillment of covenants or agreements by Glacier and breaches of or inaccuracies in Glacier's representations or warranties contained in the Merger Agreement.</footnote>
        <footnote id="F2">The Charles A. Norris &amp; Margaret T. Norris TR UA 18-Jun-02 Norris Trust (the &quot;Trust&quot;) acquired 274,045 shares of Primo Water Corporation's (&quot;Primo&quot;) common stock in connection with the acquisition of Glacier Water Services, Inc. (&quot;Glacier&quot;) by Primo on December 12, 2016 (the &quot;Merger&quot;). For each share of Glacier common stock, the Trust received approximately $12.18 in cash, 0.87 of a share of Primo common stock, and a warrant to purchase 0.55 of a share of Primo common stock.  Pursuant to the Agreement and Plan of Merger (the &quot;Merger Agreement&quot;) entered into on October 9, 2016, 194,572 of such shares of Primo common stock received by the Trust were deposited into escrow and are subject to forfeiture during the one-year period ending on December 12, 2017 to satisfy claims with respect to breaches, violations or non-fulfillment of covenants or agreements by Glacier and breaches of or inaccuracies in Glacier's representations or warranties contained in the Merger Agreement.</footnote>
        <footnote id="F3">The warrants vest and become exercisable as follows: one-third of the warrants will vest on each of June 12, 2017, September 12, 2017 and December 12, 2017.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ David J. Mills by power of attorney for Charles A. Norris</signatureName>
        <signatureDate>2016-12-14</signatureDate>
    </ownerSignature>
</ownershipDocument>
