In a statement published on its website, the club said: “Fiorentina are profoundly shaken and forced to announce that their captain Davide Astori has died.
“For this terrible and delicate situation, and above all out of respect for his family, we appeal to the sensitivity of the media.”
A club spokesman said he could not give a cause of death ahead of a post-mortem. Italian media reported that Astori died of a heart attack during the night.
The 31-year-old, who has a two-year-old daughter, was staying in a hotel in Udine to prepare for Sunday’s match against Udinese, which has been postponed.
The centre-back had been capped 14 times by Italy and enjoyed a professional career spanning 12 years.
He started out at AC Milan, where he never played a Serie A match, before moving to Cagliari, the club where he made his big breakthrough.
He made 174 appearances for the Sardinians in a six-year spell, during which he made his national team debut.
In 2014, he was sent on loan to Roma and a year later made a similar transfer to Fiorentina.
Astori had established himself as a vital member of the squad and appeared 27 times for the side, ranked 10th in the Serie A standings this term.
Tributes to the player have been posted on social media. AC Milan tweeted: “A man who loved football and who grew up as a footballer with us. AC Milan are shocked by the passing of Davide Astori.
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“It is with greater sadness that we offer our deepest condolences to his family and close loved ones and the ACF Fiorentina.”
Chelsea FC tweeted: “Everybody at Chelsea Football Club is shocked at the sudden death of Fiorentina captain Davide Astori. Our thoughts are with his family, friends and team-mates at this time.”