An autopsy will be carried out in Udine on Tuesday morning by Carlo Moreschi and Gaetano Thiene after head prosecutor Antonio De Nicolo confirmed that investigations have been opened to see if anyone could be found culpable in Astori's death.
The 31-year-old was married with a daughter and had made 289 appearances in Italy's top division.
Radja Nainggolan, Astori's former Cagliari teammate wrote on Instagram: "A great player, but even more than that, a great person".
Meanwhile, fans of the Italian club have started to pay their respects to Astori by leaving tributes and flowers outside the club's stadium, Stadio Artemio Franchi.
Astori was capped 14 times internationally and has also played for the likes of AC Milan, Cagliari and Roma.
According to the Associated Press, Astori's body has been taken to the Santa Maria della Misericordia Hospital for an autopsy.
The remainder of Serie A's slate of games was postponed after news of Astori's passing was announced by Fiorentina, with players from around the world expressing their shock and sadness at his untimely passing.
His wife was informed of the news by Fiorentina directors who visited her personally, while Astori's parents, who live in Bergamo, were told on the telephone.
Italy visit Wembley later this month for a friendly with England and the Football Association has said it will honour Astori, saying it was "truly saddened" by the news. "This news really hurt me and it's very hard in this moment to find the right words for the family".
Buffon called Astori "a great man", while Bonucci recalled their times together. "You've been one of the best sportspeople I've ever met". Italy would go on to win the match on penalty kicks.