Astori was found in the early hours of Sunday morning in his hotel room in Udine, where the team was staying ahead of an Italian league match.
Fiorentina captain and defender Davide Astori died of a sudden illness on Sunday morning at the age of 31, the Serie A club said, leaving Italian football in a state of shock.
Serie A announced that all of Sunday's matches, including the derby between AC Milan and Inter Milan, would be postponed.
"Fiorentina is deeply upset to have to announce that its captain Davide Astori has passed away, victim of a sudden illness," said the statement.
"Due to the terrible and delicate situation, and above all for the respect of his family, an appeal is made to everyone's sensibility."
Italian media said that Astori was found dead in his hotel room.
Astori joined Fiorentina on loan in August 2015 and the club signed him outright one year later. He previously spent six seasons at Cagliari and one on loan at AS Roma.
He made 14 appearances for Italy between 2012 and 2017.
"It seems impossible. I'm in a state of disbelief and I cry with his family and all for Fiorentina. Goodbye captain" said former Italy Prime Minister Matteo Renzi.
In announcing the postponement of Sunday's games, Serie A said: "Shocked by the tragic news, the whole family of the Lega Serie A unites around the family of Davide Astori and Fiorentina FC."
AC Milan coach Gennaro Gattuso had asked before the announcement for all games to be called off. "I can't think of the derby after a tragedy like that," he said on Twitter.