The two teams were due to meet at the Allianz Arena with the tie finely balanced at 1-1 after Cristiano Ronaldo scored a late penalty to rescue a draw in the first leg.
However, the game is the latest in Italy to be called off after five Serie A matches were postponed at the weekend, including Juventus' key clash with Inter Milan at the top of the table.
The AC Milan team bus had already arrived in Turin when the announcement was made. The game has been postponed "to an unknown future date," per Football Italia.
Juventus head of communications, Claudio Albanese, has said the authorities have the support of the Italian champions, per Goal's Sam France.
He said: "Juventus respects any decision taken by the authorities, public health is also a priority good for society."
Coronavirus has caused chaos with fixtures in Italy already and seen the government issue a decree suspending sporting events in all affected regions until March 8, per the Guardian.
The postponements will cause problems as the season needs to finish by 24 May due to the summer's European Championship which is scheduled to begin on June 12, per the report.
News agency ANSA has reported the government are also considering suspending all sporting events in the country for a month, per Football Italia.
Inter Milan president Steven Zhang has criticised Serie A president Paolo Dal Pino for their handling of the situation in a post on Instagram, per ESPN's Gabriel Marcotti:
An emergency meeting involving all 20 Serie A clubs will be held on Wednesday to discuss scheduling and how to deal with the current situation, per Football Italia.
The other Coppa Italia semi-final between Napoli and Inter Milan is still scheduled to go ahead at the Stadio San Paolo on Thursday. Napoli lead 1-0 from the first leg at the San Siro.