The fixture was set to kickoff at 21:00 local time after the first leg ended in a 1-1 draw at the San Siro on February 13.
Initially set to take place behind closed doors, the match was then opened to fans from Piedmont after a lifting of restrictions. However, the decision would have prevented fans from Lombardy, Emilia-Romagna and Veneto from attending as the areas are seen as hotbeds of the coronavirus outbreak.
However another meeting with local authorities was held on Tuesday night, with the parties deciding to postpone Juventus-Milan to an unknown future date.
The decision was made just after the Milan team bus arrived in Turin.
At this time the Coppa Italia clash between Napoli and Inter set for Thursday remains unaffected. The match will be open to local supporters as fans from Lombardy are not allowed to travel to the game.