The club announced the 31-year-old had died early on Sunday, just hours before they were due to face Udinese away from home.
A statement posed by Serie A's official Twitter account later said: "All matches scheduled for today [Sunday] are postponed, as a sign of mourning."
Sconvolta dalla tragica notizia, tutta la famiglia della Lega Serie A si stringe attorno alla famiglia di Davide Astori e alla @acffiorentina.
Tutte le gare in programma oggi sono rinviate in segno di lutto.
Ciao Davide. pic.twitter.com/KWa4P0dPHc — Serie A TIM (@SerieA_TIM) March 4, 2018
According to local reports in Udine, Astori passed away in his sleep at the La di Moret hotel, where Fiorentina where staying ahead of the match.