Astori is reported to have died suddenly on Sunday morning in a Udine hotel, where La Viola were basing themselves ahead of Sunday’s Serie A match.
All of Sunday’s Serie A games have been postponed as a show of respect for the player.
A club statement read: “Fiorentina is deeply saddened to announce that our captain Davide Astori has passed away, after suffering a sudden illness.
“For this terrible and delicate situation, and above all out of respect for his family, we appeal to the sensitivity of the media.”
The central defender began his career with AC Milan, but after failing to break into the first team he moved to Cagliari in 2008 and made 174 appearances for the Italian side during a six-year spell.
Following loan stints with Roma and Fiorentina, Astori made his move to Florence permanent in 2016 – scoring three goals in 58 games.
Astori was capped for Italy 14 times, making his debut in a 2-0 friendly win over Ukraine in 2011.
The FA say they are planning a tribute to Astori when Italy travel to Wembley for a friendly later this month.