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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2017-06-01</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001268533</issuerCik>
        <issuerName>TORTOISE ENERGY INFRASTRUCTURE CORP</issuerName>
        <issuerTradingSymbol>TYG</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001280972</rptOwnerCik>
            <rptOwnerName>MALVEY KENNETH P</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>11550 ASH STREET</rptOwnerStreet1>
            <rptOwnerStreet2>SUITE 300</rptOwnerStreet2>
            <rptOwnerCity>LEAWOOD</rptOwnerCity>
            <rptOwnerState>KS</rptOwnerState>
            <rptOwnerZipCode>66211</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>1</isOther>
            <officerTitle></officerTitle>
            <otherText>Member of Investment Committee</otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Shares</value>
            </securityTitle>
            <transactionDate>
                <value>2017-06-01</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>5</transactionFormType>
                <transactionCode>L</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>177.21</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>31.98</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>13945.73</value>
                    <footnoteId id="F2"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Shares</value>
            </securityTitle>
            <transactionDate>
                <value>2017-06-01</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>5</transactionFormType>
                <transactionCode>L</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>59.67</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>31.98</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>2972.99</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By spouse</value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Shares</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>297</value>
                    <footnoteId id="F3"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By adult child not living at home; reporting person can trade on account for adult child's benefit</value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes>
        <footnote id="F1">Automatic reinvestment of distribution by broker not made at the Tortoise Energy Infrastructure Corporation dividend reinvestment plan price.  This transaction is being voluntarily reported early on Form 4.</footnote>
        <footnote id="F2">Includes 108.71 shares acquired under the Tortoise Energy Infrastructure Corporation dividend reinvestment plan.</footnote>
        <footnote id="F3">These shares, held by adult child no longer living at home and which had been previously disclaimed, are being reported again as the reporting person has been given power to trade on this account again for adult child's benefit.</footnote>
    </footnotes>

    <ownerSignature>
        <signatureName>Kenneth P. Malvey</signatureName>
        <signatureDate>2017-08-29</signatureDate>
    </ownerSignature>
</ownershipDocument>
