Ballet star Nicoletta Manni, prima ballerina at La Scala, carried the torch through the square before lighting the cauldron, which will burn guarded 24/7 until the Opening Ceremony this 6 February at San Siro Stadium.
The relay, delayed by about an hour due to the crowd, had crossed several Milan suburbs earlier in the day.
The Milan leg marked the 60th stage of a 12,000 km journey that began in Olympia last November.
The flame is set to pass from the Duomo to Arco della Pace on Thursday before being escorted to San Siro Stadium for the 20:00 CET ceremony, covering an estimated 12 kilometres.
Organisers are refusing to name the person who will light the cauldron, prompting speculation around Italian skiing icons Alberto Tomba and Deborah Compagnoni, or Olympic gold medallist Sofia Goggia.