"For the bad and delicate situation, and above all for the respect of his family, appeal is made to everyone's sensibility", Fiorentina said.
His former side Cagliari were due to face Genoa at 11:30am but the match was postponed just minutes before kick-off as the news filtered through.
He joined Cagliari in 2008 where spent most of his career there in 174 worldwide match appearances.
After spending several years with Cagliari, Astori spent one season at Roma.
"The idea we have of the situation is that the player died of cardiac arrest by natural causes", said Udine prosecutor Antonio De Nicolo."It is unusual that such a thing should happen to a professional who is so closely monitored and showed no warning signs".
"A great player, but even more than that, a great person".
"Today we mourn the loss of Davide Astori".
Buffon, who wrote in a post on Instagram accompanied by a photo of the two players exchanging pennants before a game between their clubs, said he did not usually make a habit of expressing his feelings about others.
The centre-back had 14 caps for his country after making his debut in 2011 and had enjoyed a professional career spanning 12 years, which also took in the 2013 Confederations Cup.
"You were one of the best sports figures that I came across".
The Astori tragedy has evoked memories in Italy of the deaths of Perugia's Renato Curi in 1977, Roma's Giuliano Taccola in 1969, and, in 2012, Livorno's Piermario Morosini.
Among the other Serie A games to be postponed was Sunday evening's Milan derby between AC and Inter.
He was raised at AC Milan but never played for their senior team. The Italian is survived by his wife Francesca Fioretti, and a two-year-old daughter, Vittoria.