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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2014-08-15</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001362925</issuerCik>
        <issuerName>Planet Payment Inc</issuerName>
        <issuerTradingSymbol>PLPM</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001457240</rptOwnerCik>
            <rptOwnerName>Kersey Christopher W</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O CAMDEN PARTNERS HOLDINGS, LLC</rptOwnerStreet1>
            <rptOwnerStreet2>500 EAST PRATT STREET SUITE 1200</rptOwnerStreet2>
            <rptOwnerCity>BALTIMORE</rptOwnerCity>
            <rptOwnerState>MD</rptOwnerState>
            <rptOwnerZipCode>21202</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>1</isOther>
            <officerTitle></officerTitle>
            <otherText>See Remarks</otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001583196</rptOwnerCik>
            <rptOwnerName>TAGLER JASON</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O CAMDEN PARTNERS HOLDINGS, LLC</rptOwnerStreet1>
            <rptOwnerStreet2>500 EAST PRATT STREET SUITE 1200</rptOwnerStreet2>
            <rptOwnerCity>BALTIMORE</rptOwnerCity>
            <rptOwnerState>MD</rptOwnerState>
            <rptOwnerZipCode>21202</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>1</isOther>
            <officerTitle></officerTitle>
            <otherText>See Remarks</otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001583194</rptOwnerCik>
            <rptOwnerName>SHERMAN JOSEPH T</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O CAMDEN PARTNERS HOLDINGS, LLC</rptOwnerStreet1>
            <rptOwnerStreet2>500 EAST PRATT STREET SUITE 1200</rptOwnerStreet2>
            <rptOwnerCity>BALTIMORE</rptOwnerCity>
            <rptOwnerState>MD</rptOwnerState>
            <rptOwnerZipCode>21202</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>1</isOther>
            <officerTitle></officerTitle>
            <otherText>See Remarks</otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2014-08-15</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>23166</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.01</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>44984</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See footnote</value>
                    <footnoteId id="F1"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1997513</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See footnote</value>
                    <footnoteId id="F2"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>118496</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</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>4446267</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See footnote</value>
                    <footnoteId id="F4"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>184780</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See footnote</value>
                    <footnoteId id="F5"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes>
        <footnote id="F1">This is a restricted stock grant to Shane Kim under the Issuer's 2012 Equity Incentive Plan, and will be 100% vested on June 16, 2015, provided that Mr. Kim is still providing services to the Issuer as of such date.</footnote>
        <footnote id="F2">These securities are owned directly by Fund II-A.  The Reporting Person, CPSM, CPS III, CPS II, Fund III, Fund III-A, Fund II-B and the Managing Members may be deemed indirect beneficial owners of the securities held directly by Fund II-A as a result of their relationships described in the Remarks (below).  The Reporting Person, CPSM, CPS III, CPS II, Fund III, Fund III-A, and Fund II-B and each of the Managing Members disclaim beneficial ownership of the securities held directly by Fund II-A, except to the extent of their respective pecuniary interests therein.</footnote>
        <footnote id="F3">These securities are owned directly by Fund II-B.  The Reporting Person, CPSM, CPS III, CPS II, Fund III, Fund III-A, Fund II-A and the Managing Members may be deemed indirect beneficial owners of the securities held directly by Fund II-B as a result of their relationships described in the Remarks (below).  The Reporting Person, CPSM, CPS III, CPS II, Fund III, Fund III-A, and Fund II-A and each of the Managing Members disclaim beneficial ownership of the securities held directly by Fund II-B, except to the extent of their respective pecuniary interests therein.</footnote>
        <footnote id="F4">These securities are owned directly by Fund III.  The Reporting Person, CPSM, CPS III, CPS II, Fund III-A, Fund II-A, Fund II-B and the Managing Members may be deemed indirect beneficial owners of the securities held directly by Fund III as a result of their relationships described in the Remarks (below).  The Reporting Person, CPSM, CPS III, CPS II, Fund III-A, Fund II-A and Fund II-B and each of the Managing Members disclaim beneficial ownership of the securities held directly by Fund III, except to the extent their respective pecuniary interests therein.</footnote>
        <footnote id="F5">These securities are owned directly by Fund III-A.  The Reporting Person, CPSM, CPS III, CPS II, Fund III, Fund II-A, Fund II-B and the Managing Members may be deemed indirect beneficial owners of the securities held directly by Fund III-A as a result of their relationships described in the Remarks (below).  The Reporting Person, CPSM, CPS III, CPS II, Fund III, Fund II-A and Fund II-B and each of the Managing Members disclaim beneficial ownership of the securities held directly by Fund III-A, except to the extent of their respective pecuniary interests therein.</footnote>
    </footnotes>

    <remarks>This report is the same as the Form 4 filed by the Reporting Persons of even date and consists of two (2) parts, which together comprise a single Form 4. This is part 2 of 2.  This Form 4 is being filed jointly by Shane H. Kim, Camden Partners Strategic Manager, LLC (&quot;CPSM&quot;), Camden Partners Strategic III, LLC (&quot;CPS III&quot;), Camden Partners Strategic II, LLC (&quot;CPS II&quot;), Camden Partners Strategic Fund III, LP (&quot;Fund III&quot;), Camden Partners Strategic Fund III-A, LP (&quot;Fund III-A&quot;), Camden Partners Strategic Fund II-A, LP (&quot;Fund II-A&quot;) and Camden Partners Strategic Fund II-B, LP (&quot;Fund II-B&quot;) and Messrs. David L. Warnock, Donald W. Hughes, Christopher Kersey, Jason Tagler, and J. Todd Sherman (collectively, the &quot;Managing Members&quot; and together with Mr. Kim, CPSM, CPS III, CPS II, Fund III, Fund III-A, Fund II-A and Fund II-B, the &quot;Reporting Persons&quot;). The Managing Members are the managing members of CPS II and CPSM, which is the managing member of CPS III. CPS III is the general partner of Fund III and Fund III-A. CPS II is the general partner of Fund II-A and Fund II-B. Mr. Kim is a managing member of CPSM and a director of the Issuer.</remarks>

    <ownerSignature>
        <signatureName>/s/ J. Todd Sherman, Attorney-in-Fact for Christopher Kersey</signatureName>
        <signatureDate>2014-08-20</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>/s/ J. Todd Sherman, Attorney-in-Fact for Jason Tagler</signatureName>
        <signatureDate>2014-08-20</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>/s/ J. Todd Sherman</signatureName>
        <signatureDate>2014-08-20</signatureDate>
    </ownerSignature>
</ownershipDocument>
