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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2015-03-02</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001195933</issuerCik>
        <issuerName>INFINITY PROPERTY &amp; CASUALTY CORP</issuerName>
        <issuerTradingSymbol>IPCC</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001349257</rptOwnerCik>
            <rptOwnerName>Pitrone Scott C</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>3700 COLONNADE PARKWAY, SUITE 600</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>BIRMINGHAM</rptOwnerCity>
            <rptOwnerState>AL</rptOwnerState>
            <rptOwnerZipCode>35243</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>Sr. VP, Product Management</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2015-03-02</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>7431</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>56780</value>
                    <footnoteId id="F2"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">Represents the number of shares that the reporting person is entitled to receive on April 15, 2015 upon the conversion of 6,540 Performance Share Units awarded under the terms of the Second Amended and Restated 2008 Performance Share Plan based upon achievement of performance goals for the period beginning January 1, 2012 and ending December 31, 2014.</footnote>
        <footnote id="F2">Includes 1490.83 shares acquired through the company's employee stock purchase plan, including 65.19 shares acquired subsequent to August 5, 2014, and 1264.17 shares acquired through a dividend reinvestment plan, including 356.46 shares acquired subsequent to August 5, 2014.</footnote>
    </footnotes>

    <ownerSignature>
        <signatureName>/s/ James H. Romaker, By Power of Attorney</signatureName>
        <signatureDate>2015-03-04</signatureDate>
    </ownerSignature>
</ownershipDocument>
