The Ajax fans fought with both opposing supporters and Italians demonstrating against Enrico Letta's government in running battles throughout the day.
The supporter in the worst condition was knifed in the stomach and the others were wounded in the buttock and leg, a police spokesman said.
"The one with the stomach wound is clearly the most serious but as far as I understand it's not life threatening," he said.
All three were taken to Milan's San Carlo hospital, while a local street salesman also suffered a minor knife wound in the scuffles but was not hospitalised.
Three Ajax supporters were arrested in a separate incident for trying to rob a street kiosk.