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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2014-11-04</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001467808</issuerCik>
        <issuerName>China Cord Blood Corp</issuerName>
        <issuerTradingSymbol>CO</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001225028</rptOwnerCik>
            <rptOwnerName>MCCARTHY KENT C</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>7335 COTTONWOOD DRIVE</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>SHAWNEE</rptOwnerCity>
            <rptOwnerState>KS</rptOwnerState>
            <rptOwnerZipCode>66216</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>1</isOther>
            <officerTitle></officerTitle>
            <otherText>Member 13(d) group owning &gt;10%</otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001002078</rptOwnerCik>
            <rptOwnerName>JAYHAWK CAPITAL MANAGEMENT, L.L.C.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>5410 WEST 61ST PLACE</rptOwnerStreet1>
            <rptOwnerStreet2>SUITE 100</rptOwnerStreet2>
            <rptOwnerCity>MISSION</rptOwnerCity>
            <rptOwnerState>KS</rptOwnerState>
            <rptOwnerZipCode>66205</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>1</isOther>
            <officerTitle></officerTitle>
            <otherText>13(d) group owning &gt; 10%</otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001469684</rptOwnerCik>
            <rptOwnerName>JAYHAWK PRIVATE EQUITY, LLC</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>930 TAHOE BLVD., 802-281</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>INCLINE VILLAGE</rptOwnerCity>
            <rptOwnerState>NV</rptOwnerState>
            <rptOwnerZipCode>89451</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>0001588379</rptOwnerCik>
            <rptOwnerName>JHAB MANAGEMENT II, LLC</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>7335 COTTONWOOD DRIVE</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>SHAWNEE</rptOwnerCity>
            <rptOwnerState>KS</rptOwnerState>
            <rptOwnerZipCode>66216</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>1</isOther>
            <officerTitle></officerTitle>
            <otherText>Member of 13(d) group owning m</otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001542402</rptOwnerCik>
            <rptOwnerName>JCF CO LF, L.P.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>7335 COTTONWOOD DRIVE</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>SHAWNEE</rptOwnerCity>
            <rptOwnerState>KS</rptOwnerState>
            <rptOwnerZipCode>66216</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>1</isOther>
            <officerTitle></officerTitle>
            <otherText>Member of 13(d) group owning m</otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001469683</rptOwnerCik>
            <rptOwnerName>JAYHAWK PRIVATE EQUITY GP II, L.P.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>930 TAHOE BLVD., 802-281</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>INCLINE VILLAGE</rptOwnerCity>
            <rptOwnerState>NV</rptOwnerState>
            <rptOwnerZipCode>89451</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>0001427940</rptOwnerCik>
            <rptOwnerName>JAYHAWK PRIVATE EQUITY FUND II LP</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>930 TAHOE BLVD., 802-281</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>INCLINE VILLAGE</rptOwnerCity>
            <rptOwnerState>NV</rptOwnerState>
            <rptOwnerZipCode>89451</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>0001588328</rptOwnerCik>
            <rptOwnerName>JHAB FUND II, LLC</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>7335 COTTONWOOD DRIVE</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>SHAWNEE</rptOwnerCity>
            <rptOwnerState>KS</rptOwnerState>
            <rptOwnerZipCode>66216</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle></officerTitle>
            <otherText>Member of 13(d) group owning m</otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001624560</rptOwnerCik>
            <rptOwnerName>McCarthy Family SD, LLC</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>7335 COTTONWOOD DRIVE</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>SHAWNEE</rptOwnerCity>
            <rptOwnerState>KS</rptOwnerState>
            <rptOwnerZipCode>66216</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle></officerTitle>
            <otherText>Member of 13(d) group owning m</otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2014-11-04</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>P</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>50000</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>5.0559</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>9887192</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Explanation of Responses to Table I, Item 7</value>
                    <footnoteId id="F2"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2014-11-06</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>P</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>100000</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>5.2158</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>9987192</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Explanation of Responses to Table I, Item 7</value>
                    <footnoteId id="F2"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes>
        <footnote id="F1">Acquired by McCarthy Family SD, LLC.</footnote>
        <footnote id="F2">See Exhibit 99.1</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Kent C. McCarthy</signatureName>
        <signatureDate>2014-11-10</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>/s/ Kent C. McCarthy Manager of Jayhawk Capital Management, L.L.C</signatureName>
        <signatureDate>2014-11-10</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>/s/ Kent C. McCarthy Manager of Jayhawk Private Equity, LLC</signatureName>
        <signatureDate>2014-11-10</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>/s/ Kent C. McCarthy Manager of JHAB Management II, LLC</signatureName>
        <signatureDate>2014-11-10</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>/s/ Kent C. McCarthy Manager of Jayhawk Capital Management, L.L.C., which is the general partner of JCF CO LF, L.P.</signatureName>
        <signatureDate>2014-11-10</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>/s/ Kent C. McCarthy Manager of Jayhawk Private Equity, LLC, which is the general partner of Jayhawk Private Equity GP II, L.P.</signatureName>
        <signatureDate>2014-11-10</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>/s/ Kent C. McCarthy Manager of Jayhawk Private Equity, LLC, which is the general partner of Jayhawk Private Equity GP II, L.P., which is the general partner of Jayhawk Private Equity Fund II, L.P.</signatureName>
        <signatureDate>2014-11-10</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>/s/ Kent C. McCarthy Manager of JHAB Management II, LLC which is the manager of JHAB Fund II, LLC</signatureName>
        <signatureDate>2014-11-10</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>/s/ Kent C. McCarthy Manager of McCarthy Family SD, LLC</signatureName>
        <signatureDate>2014-11-10</signatureDate>
    </ownerSignature>
</ownershipDocument>
