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| <?xml version="1.0" encoding="windows-1252"?> |
| <ownershipDocument> |
| <schemaVersion> X0306 </schemaVersion> |
| <documentType> 4 </documentType> |
| <periodOfReport> 2021-05-07 </periodOfReport> |
| <notSubjectToSection16> 0 </notSubjectToSection16> |
| <issuer> |
| | <issuerCik> 0000884713 </issuerCik> |
| | <issuerName> Primo Water Corp /CN/ </issuerName> |
| | <issuerTradingSymbol> PRMW </issuerTradingSymbol> |
| | </issuer> |
| <reportingOwner> |
| | <reportingOwnerId> |
| | | <rptOwnerCik> 0001256736 </rptOwnerCik> |
| | | <rptOwnerName> SAVAGE GRAHAM W </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> 2021-05-07 </value> |
| </transactionDate> |
| | | <deemedExecutionDate></deemedExecutionDate> |
| | | <transactionCoding> |
| <transactionFormType> 4 </transactionFormType> |
| <transactionCode> A </transactionCode> |
| <equitySwapInvolved> 0 </equitySwapInvolved> |
| </transactionCoding> |
| | | <transactionTimeliness> |
| <value></value> |
| </transactionTimeliness> |
| | | <transactionAmounts> |
| <transactionShares> |
| <value> 7092 </value> |
| <footnoteId id="F1"/> |
| </transactionShares> |
| <transactionPricePerShare> |
| <value> 16.92 </value> |
| </transactionPricePerShare> |
| <transactionAcquiredDisposedCode> |
| <value> A </value> |
| </transactionAcquiredDisposedCode> |
| </transactionAmounts> |
| | | <postTransactionAmounts> |
| <sharesOwnedFollowingTransaction> |
| <value> 58764 </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 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 $16.92 (the closing price of the Common Shares on the New York Stock Exchange on May 7, 2021). </footnote> |
| | </footnotes> |
| <remarks></remarks> |
| <ownerSignature> |
| | <signatureName> /s/ Marni Morgan Poe, Attorney-in-Fact </signatureName> |
| | <signatureDate> 2021-05-11 </signatureDate> |
| | </ownerSignature> |
| </ownershipDocument> |
