The 31-year-old was found dead in his hotel room on Sunday just hours ahead of his side's scheduled Serie A match with Udinese.
Antonio De Nicolo has now confirmed Astori died after his heart gradually slowed to a stop, with no sign of any external causes.
Speaking to Rai, he said the autopsy indicated "cardiac death without macroscopic evidence, likely with a bradyarrhythmia basis".
He added: "From the preliminary results, it does not seem there are any external causes other than that of a natural death, but prudently our advisers say we must wait for the result of histological examinations before declaring anything definitively.
"They have asked for 60 days to complete their report and, from that point, we will have a complete picture."
A funeral for Astori is now expected to be held on Friday (AEDT).
De Nicolo said on Tuesday (AEDT) that criminal proceedings were opened "on the hypothesis of manslaughter against unknown persons", as part of the investigation into how Astori died so suddenly.
The manslaughter process was understood to have been initiated to allow a full autopsy to take place and was not linked to any individual, with De Nicolo describing the theory as "purely abstract", according to ANSA.
Tributes have continued to come in from across the football world, with Paris Saint-Germain's Dani Alves describing Astori as "an admirable person", while former AC Milan chief executive Adriano Galliani said the former Rossoneri youth player was "one of our boys".
A minute's silence will be held before all UEFA Champions League and Europa League matches this week, while both Fiorentina and Cagliari have retired the No.13 shirt as a mark of respect.