Danica Patrick -- Topless Selfie ... On Sports Illustrated Website

So ... Danica Patrick's exposed nipple is hanging out on a Sports Illustrated website.

The racy pic of the NASCAR driver is featured in a "Throwback Thursday" photo gallery on S.I.'s "Swim Daily" website ... which features a "selfie" style photo shoot of Danica from 2008.

We called S.I. to find out if it was a mistake ... or one of those intentional "nipples are artsy" sort of things ... but so far, we haven't heard back.