The Swede was dismissed 17 minutes from time for striking Marco Rossi in the chest in an off-the-ball incident and Serie A said in a statement on Monday that its disciplinary commissioner had ruled the offence serious enough to merit a three-game ban.
The suspension of their main attacker comes at a terrible time for leaders Milan with just nine games left in the season.
Milan lead champions Inter by five points but Ibrahimovic will now be forced to sit out next weekend's trip to Palermo, the derby with Inter and the trip to Fiorentina.
Milan, who only have Alexandre Pato as a fit out-and-out striker, said in a statement they would appeal the severity of the ban.
Ibrahimovic has looked out of sorts in recent weeks after a strong start to his Milan career having joined from Barcelona last year after just one season in Spain following his move from Inter.
He struggled in last week's Champions League elimination at Tottenham Hotspur and looked frustrated throughout the home draw with Serie A's bottom side Bari.
It was a busy day for Serie A's disciplinary commissioner with Parma's Daniele Galloppa and Lazio's Stefan Radu also given three-game bans for similar offences.
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