The Ligue de Football Professionnel (LFP) docked Nice two Ligue 1 points, one of which was suspended, due to their involvement in the chaotic scenes with Marseille last month.
The August 22 clash was suspended and then abandoned after home fans stormed the Allianz Riviera pitch in response to Marseille's Dimitri Payet, who was hit on the back of the neck, throwing a bottle back into the Nice crowd.
The LFP had summoned the two teams to a disciplinary hearing on August 25 to explain the unsavoury scenes, which saw a melee break out on the pitch and subsequently in the dugout.
On Wednesday, the LFP announced its decision to punish Nice with a one-point deduction, while also subjecting the French club to three games behind closed doors.
For inciting the crowd, Marseille star Payet received a one-game suspension while team-mate Alvaro Gonzalez faces a two-match ban for also provoking the home fans.
The fixture with rivals Marseille, which failed to be completed as the visitors refused to come back onto the pitch, will also be rearranged and played on a neutral ground without supporters in attendance.
"After reading the investigation report in the presence of the two clubs, the Commission decided to replay the match on a relocated field," the LFP said in a statement midweek.
"In addition, two penalty points were imposed on OGC Nice, including one suspended point."
Marseille physio Pablo Fernandez was caught on camera punching a Nice fan and, after already being suspended indefinitely by the LFP, he will not return to the touchline until June 30th 2022.
Of Payet and Gonzalez, France football's governing body added: "Regarding the players, defender Alvaro Gonzalez received two games of suspension.
"As for his team-mate Dimitri Payet, he was sanctioned with a suspended match."
Nice have won two of their opening three league matches following an unbeaten start to the season, while Marseille also boast the same record.