The 31-year-old former Italy international was found dead at his team's hotel on Sunday morning, just hours before Fiorentina were due to face Udinese.
It was initially suspected that Astori has passed away following a cardiac arrest, but Italian authorities have now confirmed that they have opened criminal proceedings into the case.
"We have opened criminal proceedings over the hypothesis of manslaughter," Antonio De Nicolo, Udine chief prosecutor, told Radio Rai.
"For now, it's been brought against unknown persons. We've arranged an autopsy, which will be performed soon."
De Nicolo added in quotes published by Italian news agency ANSA: "An inquiry has been opened for culpable homicide against persons unknown. It is a duty to ascertain if the death of Astori came about through tragic fatality or if someone could have foreseen something.
"At this moment no-one has responsibility for anything which would seem to us to amount to something. It permits us to individualise responsibility if there is any."
All of Sunday's Serie A games were postponed following the death of Astori, who won 14 caps for Italy during his career.