Domestic news agency ANSA said the fans had been stabbed in separate incidents close to the San Siro stadium and were being treated in the city's San Carlo Hospital.
One fan, who had been stabbed in the buttocks, is not in danger while the other was in a "serious" condition after being stabbed in the stomach, according to the report.
The report added that another Ajax fan, who had been stabbed in the thigh, and a passerby who had been stabbed in the leg had also been admitted to hospital.
All three Ajax fans were aged 18 to 32, added the report.
Fans of the Dutch side were involved in scuffles earlier in the day in Milan, notably when Ajax fans fought with a group of demonstrators who had congregated near Piazza Loreto.
Around 300 fans of the Dutch side were also seen in the centre of Milan near the city's famous Duomo cathedral, where they split into two groups. It was reported that several shop windows were damaged.
Hundreds of police, most with riot gear, were deployed around the stadium and were shepherding Ajax fans into special buses as soon as they exited the metro at Piazza Lotto, according to a reporter at the scene.
Less than an hour before kick-off, security personnel around the stadium had to be called into action to contain rowdy fans of the Dutch club as they tried to enter the stadium.
AC Milan require only a draw against Ajax to advance to the last 16 of the Champions League while Ajax need a win if they are to jump up to second place in Group H and join already qualified Barcelona in the knockout phase.