The 19-year-old, who also scored in the 4-2 win, was sent off for pushing over Teji Savanier after the Nimes player hacked him to the ground.
The French champions will be without Mbappe for Ligue 1 games against Saint-Etienne on September 14, Rennes on September 23 and Reims three days later.
The ban does not affect Mbappe’s participation in PSG’s mouthwatering Champions League opener against last season’s runners-up Liverpool at Anfield on Tuesday, September 18.
Savanier, who was also dismissed by referee Jerome Brisard after the incident, has been handed a five-match suspension.
Mbappe had already been booked in the first half of the encounter last Saturday for taking the ball away before a Nimes free-kick.
It is the second red card of Mbappe’s young career after he was sent off in January for a bad foul on Rennes’ Ismaila Sarr during a French League Cup semi-final.
As he is currently with the France squad preparing for Thursday’s UEFA Nations League opener against Germany in Munich, he was not present at Wednesday’s disciplinary hearing.
Mbappe was named the best young player of the tournament after scoring four goals as France won the World Cup for the second time in July, becoming only the second teenager after Brazilian legend Pele to net in a World Cup final.
He has already scored four goals in just three appearances for PSG this season.
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