The victim was stabbed twice in the leg and taken to Milan's Policlinico hospital for treatment, police said. Italian media said he was a 34-year-old Frenchman.
He was injured when a group of around 50 Milan fans clashed with visiting PSG supporters shortly after midnight in the city's canal district, a popular spot for nightlife.
Two police officers were also hurt after police baton-charged the French fans to try to restore order.
"Football for us is passion, not hate. Sport is supposed to unite, not divide," the club said in a post on social media site X, the message written in English, Italian and French.
AC Milan host PSG at the San Siro stadium on Tuesday evening.
A fan of English club Newcastle United was stabbed in Milan in September before his team's Champions League game with AC Milan.
