At least two bodies were found in the apartment in Saint-Denis, north of Paris, after a shootout with police, but they have not yet been identified, prosecutor Francois Molins told a press conference.
He said intelligence had led investigators to believe Abaaoud, a leading Islamic State extremist, could have been in the apartment.
In a ferocious shootout, a woman detonated her suicide vest and a body was found riddled with bullets and was "not in a state that allows it to be identified", Molins said.