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

    <schemaVersion>X0304</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2012-03-09</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0000008947</issuerCik>
        <issuerName>AZZ INC</issuerName>
        <issuerTradingSymbol>AZZ</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001251421</rptOwnerCik>
            <rptOwnerName>DINGUS DAVID H</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>ONE MUSEUM PLACE, SUITE 500</rptOwnerStreet1>
            <rptOwnerStreet2>3100 WEST 7TH STREET</rptOwnerStreet2>
            <rptOwnerCity>FORT WORTH</rptOwnerCity>
            <rptOwnerState>TX</rptOwnerState>
            <rptOwnerZipCode>76107</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>Chief Executive Officer</officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>COMMON STOCK</value>
                <footnoteId id="F1"/>
            </securityTitle>
            <transactionDate>
                <value>2012-03-09</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>10865</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>51.34</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>138397</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>COMMON STOCK</value>
                <footnoteId id="F2"/>
            </securityTitle>
            <transactionDate>
                <value>2012-03-09</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>D</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>3417</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>51.34</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>134980</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes>
        <footnote id="F1">Upon the vesting of restricted stock units on March 1, 2012 granted to the reporting person on March 1, 2009, the reporting person received 10,865 shares of common stock on March 9, 2012.</footnote>
        <footnote id="F2">Of the 10865 shares of common stock received on March 9, 2012, the reporting person disposed of 3417 shares of common stock on March 9, 2012 to satisfy tax withholding obligations.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>DANA PERRY</signatureName>
        <signatureDate>2012-03-12</signatureDate>
    </ownerSignature>
</ownershipDocument>
