Conte also extended a series of strict quarantine measures, which includes a ban on public gatherings.
Italy's Olympic committee recommended the move after a special meeting was held.
Here are further details.
How the coronavirus affected Serie A matches?
The announcement from CONI came after the Serie A game between Sassuolo and Brescia kicked off. The game carried on and Sassuolo won 3-0.
Besides that, Juventus' match against Inter on Sunday saw the same being played behind closed doors.
The Italian champions won the match 2-0 to go top.
Also, Parma's fixture against SPAL on Sunday kicked off 75 minutes late.
Italy worst hit by coronavirus in Europe
Italy are the worst hit by coronavirus so far in Europe. Over 9,000 confirmed cases have already been registered and there have been more than 450 deaths as well. "This situation has no precedent in history," a CONI statement read.
There's no reason for the games to continue: Italian PM
"There's no reason for the games to continue," Mr Conte said. "The fans will have to deal with it. We won't even allow gyms to be used."
Besides Serie A football division, the Six Nations rugby union matches are also suspended until April 3.
Meanwhile, the Italian Olympic Committee said earlier that the decree will not include international competition "for clubs or national teams".
Indian Wells tennis tournament got cancelled on Monday