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

    <schemaVersion>X0303</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2010-11-30</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0000046640</issuerCik>
        <issuerName>HEINZ H J CO</issuerName>
        <issuerTradingSymbol>HNZ</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001375799</rptOwnerCik>
            <rptOwnerName>Weinstein Michael Feder</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>INOV8 BEVERAGE COMPANY LLC</rptOwnerStreet1>
            <rptOwnerStreet2>350 THEODORE FREMD AVENUE</rptOwnerStreet2>
            <rptOwnerCity>RYE</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10580</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle></officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock, $.25 Par Value</value>
                <footnoteId id="F1"/>
            </securityTitle>
            <transactionDate>
                <value>2010-11-30</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>147</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>48.27</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>23619</value>
                    <footnoteId id="F2"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes>
        <footnote id="F1">Deferred stock units acquired as a result of previously elected deferral of cash compensation.</footnote>
        <footnote id="F2">Includes 20,619 shares of deferred stock units acquired as a result of previously elected deferral of cash and equity compensation and dividend equivalent reinvestment on those deferred stock units and 3,000 shares of common stock.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Patrick J. Guinee, Attorney-in-Fact for Michael F. Weinstein</signatureName>
        <signatureDate>2010-12-01</signatureDate>
    </ownerSignature>
</ownershipDocument>
