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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2012-12-21</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0000792985</issuerCik>
        <issuerName>HEALTH MANAGEMENT ASSOCIATES, INC</issuerName>
        <issuerTradingSymbol>HMA</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001138995</rptOwnerCik>
            <rptOwnerName>GLENVIEW CAPITAL MANAGEMENT LLC</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>767 FIFTH AVENUE</rptOwnerStreet1>
            <rptOwnerStreet2>44TH FLOOR</rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10153</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle></officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001228603</rptOwnerCik>
            <rptOwnerName>ROBBINS LAWRENCE M</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>767 FIFTH AVENUE, 44TH FLOOR</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10153</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle></officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Class A Common Stock, $0.01 par value</value>
            </securityTitle>
            <transactionDate>
                <value>2012-12-21</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>P</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>450000</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>9.07</value>
                    <footnoteId id="F2"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>34059503</value>
                    <footnoteId id="F1"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                    <footnoteId id="F1"/>
                    <footnoteId id="F3"/>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See footnotes</value>
                    <footnoteId id="F1"/>
                    <footnoteId id="F3"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes>
        <footnote id="F1">These shares of the Issuer's Class A Common Stock, $0.01 par value per share (the &quot;Shares&quot;) were purchased for the accounts of Glenview Capital Partners, L.P., Glenview Capital Master Fund, Ltd., Glenview Institutional Partners, L.P., Glenview Offshore Opportunity Master Fund, Ltd., Glenview Capital Opportunity Fund, L.P., and GCM Opportunity Fund, L.P.</footnote>
        <footnote id="F2">This price reflects the weighted average purchase price for open-market purchases of Shares made by the Reporting Persons on December 21, 2012 within a $1.00 range. The actual prices for these transactions range from $9.00 to $9.08, inclusive. The Reporting Persons further undertake to provide upon request by the Commission staff, the Issuer, or a security holder of the Issuer, full information regarding the number of shares purchased at each separate price.</footnote>
        <footnote id="F3">Glenview Capital Management, LLC serves as investment manager to each of Glenview Capital Partners, L.P., Glenview Capital Master Fund, Ltd., Glenview Institutional Partners, L.P., Glenview Offshore Opportunity Master Fund, Ltd., Glenview Capital Opportunity Fund, L.P., and GCM Opportunity Fund, L.P. Mr. Robbins is the Chief Executive Officer of Glenview Capital Management, LLC.  Each Reporting Person disclaims beneficial ownership of the Shares except to the extent of his or its pecuniary interest therein, and this report shall not be deemed an admission that such Reporting Person is the beneficial owner of the Shares for purposes of Section 16 of the Securities Exchange Act of 1934, or for any other purpose.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Mark J. Horowitz, Chief Operating Officer and General Counsel of Glenview Capital Management, LLC and attorney-in-fact for Lawrence M. Robbins</signatureName>
        <signatureDate>2012-12-27</signatureDate>
    </ownerSignature>
</ownershipDocument>
