"Fiorentina are profoundly shocked to have to announce the death of captain Davide Astori after a sudden illness," the Serie A club said on Twitter.
The 31-year-old international defender was found dead in his hotel room in Udine, and his death is not being treated as suspicious.
The soccer star, who leaves behind a two-year-old daughter, was in Udine to prepare for Sunday's match against Udinese.
The game between Udinese and Fiorentina, where Mr Astori was due to play, had been called off in the morning, as had the early kick off between Genoa and Cagliari, which was abandoned when players learned the news while warming up on the pitch.
Fiorentina called on the media to respect Mr Astori's family in what it called a "terrible and delicate situation".
The Italian league postponed all seven Serie A matches scheduled for Sunday following Mr Astori's death.