The dispute broke out between the two visiting fans after Milan players threw shirts and shorts into the stands after the final whistle following their 3-2 away win.
It continued outside the Stadio Dall’Ara with one fan being stabbed in the abdomen and taken to hospital in a serious condition.
The argument was over who had caught one of the players’ shorts, Gazzetto Dello Sport said, quoting local reports.
Former European giants AC Milan got back-to-back Serie A wins for just the second time this season to move up to 10th place in the Italian league.