Nice have been docked two points, one of which is suspended, and must replay their Ligue 1 game with Marseille after crowd trouble led to the match on 22 August being abandoned.
Payet, team-mate Alvaro Gonzalez and Marseille coach Pablo Fernandez have all been sanctioned.
The match will be replayed behind closed doors and at a neutral location.
Nice’s punishment included a total of three games to be played behind closed doors.
The Ligue de Football Professionnel (LFP) announced its disciplinary decisions on Wednesday night with Payet handed a suspended one-match ban.
The Frenchman’s team-mate Alvaro Gonzalez has been banned for two matches while Marseille physio Pablo Fernandez has been given a nine-month touchline suspension, until 30 June 2022.
The match at Nice’s Allianz Riviera stadium was attended by a crowd of more than 32,000 with spectators allowed back inside grounds in France after the majority of the 2020-21 season was played behind closed doors due to coronavirus restrictions.
However, with Nice leading 1-0, it was abandoned in the 75th minute after fans stormed the pitch when Payet launched a bottle back into the stands having been struck in the back with it as he prepared to take a corner.
After a long delay, Nice’s players came out to finish the game – but Marseille’s players refused to.
Authorities in France subsequently ordered a four-match stand closure and arrested a man.
The incident occurred two weeks after Marseille’s 3-2 win at Montpellier was also held up when fans pelted the pitch with bottles.
That game, on 8 August, was halted in the 89th minute after Marseille substitute Valentin Rongier was hit on the head and Montpellier’s Florent Mollet was also hit as he prepared to take a corner.
Nice’s 4-0 win over Bordeau on 28 August – their first game at home since the Marseille match – was played without fans.