One supporter suffered serious injuries after being stabbed in the stomach, but his condition is "not life threatening". All three were taken to Milan's San Carlo hospital.
A spokesman for Milan police told BBC Sport: "The one with the stomach wound is clearly the most serious but as far as I understand it's not life threatening."
A street salesman suffered a minor knife wound during the pre-match violence near the city's Piazza Lotto but did not require hospital treatment.
According to reports in the Gazzetta dello Sport, three Ajax fans were arrested for their involvement in the scuffles.
On the pitch, Milan secured the point they needed from the goalless draw to progress to the last 16 of the Champions League at the Dutch club's expense.