The attack happened as travelling AC Milan fans made their way back to the coaches that had brought them to the city for the final of the Italian Cup, which Milan lost to Juventus in extra time, Ansa reported.
The two victims, aged 26 and 40, were stabbed amid a brawl during which the windows of the bar were also damaged.
The exact motive for the attack is still unknown.
The two victims were rushed to hospital and their condition is said to be serious but not life-threatening.
Following the attack, police stopped three coaches of Milan fans as they left the city – identifying 200 fans on board and arresting a 19-year-old who was later charged with attempted murder.
As police searched the buses they found several of the fans to be in possession of knives, baseball bats, screwdrivers, marijuana, smoke bombs and fireworks.
A further 70 fans were arrested and charged for hooliganism-related offences.