In the Instagram post, the 38-year-old says he'd made a "bad error of judgement".
Photos have been leaked online which seem to show him in bed with a woman.
He says he has "no excuses" but doesn't want anyone to make any money from his mistakes.
The star, who's one of the most influential comedians on the planet, posted the emotional video over the weekend.
Kevin Hart doesn't say exactly what he's done, but according to entertainment website TMZ the video of him with a woman is "sexually suggestive".