The men’s and women’s contests were initially set to take place behind closed doors in order to curb the spread of the virus.
Italy is the worst-hit European country with more than 3,000 cases.
Ireland’s Six Nations games at home to Italy on 7 and 8 March were postponed last week.
Six Nations officials will meet on Thursday after the Italian government ordered all sporting fixtures in the country to be held behind closed doors until 3 April as part of measures to contain the outbreak.
The decree, announced by Italian Prime Minister Giuseppe Conte, affects all areas of the country, including those places were the virus has not been found.
Playing the men’s match behind closed doors would have meant the Italian Rugby Federation missing out on the ticket revenues from the 73,000-capacity Stadio Olimpico. The women’s match was due to be played at the Stadio Plebiscito, a venue in Padua which holds about 10,000.
With their away match against Ireland this weekend already postponed, Italy’s Six Nations campaign is now effectively over until their final two fixtures can be rearranged.
Sergio Parisse, their talismanic captain and winner of 142 caps, had planned to mark his international retirement with a farewell appearance against England. The 36-year-old’s previous plans to bow out of Test rugby in his country’s final Rugby World Cup match against the All Blacks in October were wrecked by Typhoon Hagibis, which caused that pool game to be cancelled.