The France international has already served a one-game ban but will be unavailable to Marseille for matches against Rennes, Amiens and Strasbourg, the Ligue de Football Professionnel confirmed.
Payet had been booked for a foul on Montpellier's Hilton and he responded angrily towards referee Amaury Delerue, who produced a second yellow card.
The 32-year-old, who has scored two Ligue 1 goals this season, will be back to face Paris Saint-Germain in Le Classique at the Parc des Princes on October 27.
There were three red cards in the game and Marseille defender Boubacar Kamara has been banned for two matches for his sending-off against Montpellier.
Jordan Ferri was also sent off after a scuffle with Kamara in the closing stages and the Montpellier midfielder will serve a three-match suspension.
Marseille will also be without Kevin Strootman for their Ligue 1 match against Amiens due to an accumulation of yellow cards.