Ibrahimovic was dismissed shortly before the end of the game after he made a comment in the direction of the assistant referee. He had since claimed that he "made a comment to myself - it was not directed at the referee or his assistant".
Ibrahimovic, making his first appearance following a two-match suspension, had been booked for a foul in the 77th minute but received a straight red card ten minutes later.
He had incurred a one-match ban as a result of his eight yellow card of the season, another for the red card incident and another for receiving red cards in succession games.
Milan have announced that they will appeal the suspension, which would see the striker miss games against Sampdoria, Brescia and Bologna.
Rossoneri coach Massimiliano Allegri spoke out in defence of Ibrahimovic in the wake of the incident.
"I spoke to Ibra and he told me he was muttering to himself, not to the official," Allegri said. "Often in training, Ibra mutters to himself.
"I am happy with what he has done on the pitch even if his performance was stained by the sending-off."