Ibrahimovic banned for three games
The Sweden forward was shown a red card in the 87th minute at the Stadio Artemio Franchi for saying something to the assistant referee.
Ibrahimovic's eighth yellow card of the season resulted in an automatic one-match ban, with a further game added for insulting the linesman and another one for receiving red cards in consecutive matches.
The 29-year-old had only just returned from a two-match suspension, and will now be sidelined for league games against Sampdoria, Brescia and Bologna. Milan said they would appeal the suspension.
Ibrahimovic earlier apologised to his team-mates, claiming his comment was not aimed at the official but at himself. "I was angry with myself after losing possession," he said.
"I made a comment to myself - it was not directed at the referee or his assistant. I ask for forgiveness from everyone. I left the pitch without making a scene. I was looking at the officials as they were in front of me, and I did not have a gripe with him."
He added: "It was not the best time to be getting a red card, as I was returning from a suspension."
Rossoneri coach Massimiliano Allegri refused to condemn the former Barcelona striker. "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."