The Italian League said its disciplinary tribunal, basing its decision on video evidence, had found the Frenchman guilty of violent conduct in a clash with Juventus striker Marco Boriello.
In its verdict, the tribunal said Mexes had punched Boriello in the side, knocking him to the ground.
Milan's top-scorer Zlatan Ibrahimovic has just completed a three-match ban for slapping an opponent in a game against Napoli.
Juventus were fined 10,000 euros after their fans chanted racist insults at Milan players during the same game while Lazio were fined the same amount for ethnic insults by their fans against Fiorentina.
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.