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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2014-11-17</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>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>0001542402</rptOwnerCik>
            <rptOwnerName>JCF CO LF, L.P.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>930 TAHOE BLVD.</rptOwnerStreet1>
            <rptOwnerStreet2>802-281</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>1</isOther>
            <officerTitle></officerTitle>
            <otherText>Member 13(d) group owning &gt;10%</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 13(d) group owning &gt;10%</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>1</isOther>
            <officerTitle></officerTitle>
            <otherText>Member 13(d) group owning &gt;10%</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>1</isOther>
            <officerTitle></officerTitle>
            <otherText>Member 13(d) group owning &gt;10%</otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2014-11-17</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>P</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>26754</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>4.7000</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>10013946</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Footnote</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>2014-11-19</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>/s/ Kent C. McCarthy Manager of Jayhawk Capital Management, L.L.C</signatureName>
        <signatureDate>2014-11-19</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>/s/ Kent C. McCarthy Manager of Jayhawk Private Equity, LLC</signatureName>
        <signatureDate>2014-11-19</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>/s/ Kent C. McCarthy Manager of JHAB Management II, LLC</signatureName>
        <signatureDate>2014-11-19</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>2014-11-19</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>2014-11-19</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>2014-11-19</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>2014-11-19</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>/s/ Michael D. Schmitz Manager of McCarthy Family SD, LLC</signatureName>
        <signatureDate>2014-11-19</signatureDate>
    </ownerSignature>
</ownershipDocument>
