The centre-back was shown a straight red card by referee Paolo Mazzoleni after grabbing Stefano Mauri by his throat in the closing stages of the game, only to then completely lose his temper and proceed to scrap with both Mauri and Lorik Cana.
Mexes apologised for his behaviour on Monday, but has nonetheless been slapped with a heavy suspension for his actions.
The 32-year-old will consequently miss the Serie A games against Parma, Juventus, Empoli and Cesena.
Mexes has made nine appearances for Milan in Serie A this term, collecting four yellow cards and one red card in the process.
The San Siro side have been struggling to find their best form under Inzaghi and currently sit 11th in the Serie A table with 26 points from 20 games.
