The 28-year-old was sent off at the end of Le Classique for striking Marseille's Álvaro González as a full-scale brawl broke out in injury time that saw five players red carded.
His teammates Layvin Kurzawa and Leandro Paredes were also given six and two-game bans respectively, while Marseille's Jordan Amavi received a three-game ban and Dario Benedetto a one-game ban.
Neymar and Paredes, who also both received a suspended sanction of an additional one-match ban, will be available to play again against Stade de Reims on September 27.
PSG's Angel Di Maria has also been summoned to a disciplinary hearing next Wednesday.
The Ligue de Football Professionnel (LFP), French football's governing body, also announced it would investigate Neymar's claims he was the target of a racist slur during the French champions' 1-0 defeat.
The player at the center of the storm is González. The Spanish defender has denied the claim, saying on Twitter there is "no place for racism" and that he has a "clean career."
In a series of tweets after Sunday's game, Neymar claimed he had been called a "monkey son of a b*tch," and although he didn't name González, he later replied to the Spaniard on Twitter and accused him of "bringing racism into our lives."
PSG offered support for its player: "There is no place for racism in society, in football or in our lives," the club said in a statement on Monday, adding that it "calls on everyone to speak out against all forms of racism throughout the world."
Marseille named González in its statement but did not acknowledge the allegation of him making a racist remark, saying the Spanish defender was "not racist, as he has shown through his daily behavior since joining the club, and as his teammates have already confirmed.
"This controversy is serious and has already produced serious consequences. The club condemns the dissemination of the private telephone numbers of Alvaro González and his relatives on Brazilian media and social networks overnight, giving rise to constant harassment -- including death threats."