Beckham was given his marching orders in the last minute - six minutes after being introduced as a late substitute in Annecy - for a dangerous lunge on Youssef Adnane, with fellow midfielder Marco Verratti having also been dismissed.
Evian striker Saber Khelifa and PSG goalkeeper Sirigu were then involved in an altercation which saw both also red-carded as skirmishes ensued after the full-time whistle.
The disciplinary commission of the Ligue de Football Professionnel (LFP) dished out two-game bans to Sirigu, Verratti, and Khelifa, with the former having risked further punishment for refusing to return to the pitch to be shown the red card by referee Olivier Thual.
The bans mean Sirigu, Verratti and Beckham will all miss this weekend's potential title-decider at the Parc des Princes. Victory over Valenciennes on Sunday will guarantee the championship for Carlo Ancelotti's side if Marseille fail to overcome Bastia on Saturday.
PSG assistant sporting director Olivier Letang was also suspended for a month after it emerged that he prevented Sirigu from returning to the pitch to be shown the red card.