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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2014-09-26</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001323974</issuerCik>
        <issuerName>MWI Veterinary Supply, Inc.</issuerName>
        <issuerTradingSymbol>MWIV</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001333281</rptOwnerCik>
            <rptOwnerName>Cleary James F JR</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>3041 W. PASADENA DR.</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>BOISE</rptOwnerCity>
            <rptOwnerState>ID</rptOwnerState>
            <rptOwnerZipCode>83705</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>President and CEO</officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock, par value $0.01 per share</value>
            </securityTitle>
            <transactionDate>
                <value>2014-09-26</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>3500</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>115095</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock, par value $0.01 per share</value>
            </securityTitle>
            <transactionDate>
                <value>2014-09-26</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>F</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F2"/>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>729</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>146.59</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>114366</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock, par value $0.01 per share</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1895</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Footnote</value>
                    <footnoteId id="F3"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock, par value $0.01 per share</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1895</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Footnote</value>
                    <footnoteId id="F4"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes>
        <footnote id="F1">On September 26, 2014, the Compensation Committee of MWI Veterinary Supply, Inc. (&quot;the Company&quot;) awarded Mr. Cleary a restricted stock grant of 3,500 shares.  Pursuant to the terms of such grant, the shares will vest in equal parts of 1/5 of the total per year, beginning on September 26, 2015.</footnote>
        <footnote id="F2">Surrender of shares to satisfy tax withholding obligation incident to vesting of restricted stock.</footnote>
        <footnote id="F3">Held by Teresa Cleary Children's Trust FBO Barbara Cleary for the benefit of one of Mr. Cleary's children. Mr. Cleary expressly disclaims beneficial ownership of any shares held by such trust that exceed his pecuniary interest therein.</footnote>
        <footnote id="F4">Held by Teresa Cleary Children's Trust FBO Abigail Cleary for the benefit of one of Mr. Cleary's children. Mr. Cleary expressly disclaims beneficial ownership of any shares held by such trust that exceed his pecuniary interest therein.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>Mary Patricia B. Thompson as attorney-in-fact for James F. Cleary, Jr.</signatureName>
        <signatureDate>2014-09-30</signatureDate>
    </ownerSignature>
</ownershipDocument>
