Footage showed Payet was struck on the back by the missile near the corner flag during the second half, with Nice leading through Kasper Dolberg's 49th-minute goal.
Marseille star Payet then appeared to hurl a bottle back into the crowd, then a second lying on the turf, as his team-mates reacted furiously towards the terraces.
Fans then surged to the sidelines and forced their way past stewards and onto the pitch, where a melee broke out.
The referee suspended the match as security staff attempted to restore order, but fans continued to get onto the field of play and there were further skirmishes in the dugouts as players were led towards the tunnel.
Both sides were eventually taken to the dressing rooms for nearly an hour before Nice players returned to the pitch to warm up, with the game apparently set to resume.
The match officials set up play to continue from Marseille's corner but, as the visitors had not come back onto the pitch and were apparently refusing to do so, the referee ended the game.
Marseille president Pablo Longoria told RMC Sport: "We decided not to resume the match for the safety of our players.
"The league decided as a matter of public order to resume the match. This isn't acceptable for us. It's why we decided not to resume."