Balotelli was already automatically banned for one match after picking up his fourth booking of the season in the 2-2 draw.
However, another two matches were added to his suspension on Tuesday for abusing one of the assistant referees at the end of the game.
Balotelli will miss Milan's crunch Serie A matches against Napoli and Juventus as well as the visit of Catania.
Milan have already announced they will lodge an appeal against the ban.
The Italy international has scored 10 goals in 11 games for club and country this year.
Milan are currently third in the table, four points behind Napoli in the fight for second place and a direct Champions League berth, with Juventus holding a nine-point lead at the top.