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.