The crowded tram was travelling on the line 9 route along Milan's Viale Vittorio Veneto at about 16:00 local time (15:00 GMT) when it left the track and crashed into a building.
One of the people who died, a 60-year-old man, is thought to have been a pedestrian hit by the tram, while the other fatality and most of the injured were passengers.
Numerous ambulances went to the scene as reports emerged of people trapped in the wreckage.
