Astori was found dead on Sunday morning ahead of his team's match against Udinese and De Nicolo said they want "to be absolutely sure" the 31-year-old's death was "a tragic misfortune."
"We opened an investigation for manslaughter," De Nicolo said. "This is an act required by the law in order to perform an autopsy and we want to perform an autopsy to be absolutely sure that the death of Astori was, as it seems, only a tragic misfortune.
"There are no elements to suggest that this wasn't a death of natural causes, but we want to be able to exclude categorically any other possibility, and the only way to do so is to open an investigation.
"If the autopsy will indicate that this wasn't a natural death, then we will have to look for culprits."
Football world mourns
The world of football was left in a state of shock following news of Astori's sudden death on Sunday, aged 31.
Serie A postponed all Sunday fixtures after news emerged that the Italy international had passed away from a sudden illness.
Tributes have flooded in from the international footballing community, led by legendary Italy and Juventus goalkeeper Gianluigi Buffon, who described Astori as the "perfect person" and one of the "best figures" he has come across in sport.
Astori had been expected to play against Udinese in their top-flight clash on Sunday, but was found dead in his hotel room just hours before kick-off.
Fiorentina President Andre Della Valle told reporters that Astori had been due to sign a new contract with the club on Monday that would have kept him in Florence for the rest of his playing career.
Meanwhile former Italy forward Francesco Totti, who played alongside Astori at Roma, tweeted that he was "shocked, incredulous and speechless for this tragedy."
One of the postponed fixtures on Sunday was the derby between AC Milan and Internazionale and Milan manager Gennaro Gattuso said the death put football into perspective, tweeting, "I can't think of the derby after a tragedy like that."
At Astori's former club Cagliari, players were already on the pitch ahead of their lunchtime kick-off against Genoa when the news broke.
As the announcement came that the match would be postponed, Astori's face was shown on the stadium's big screen, causing fans of both clubs to spontaneously applaud.
In England, Chelsea manager Antonio Conte spoke about the tragic news on Sky Sports ahead of his side's Premier League clash with Manchester City, saying: "I had him with the national team. It's very difficult to speak about this tragedy.
"He was a fantastic guy -- a great player but especially a fantastic guy."
The centre-back earned 14 caps for the Azzurri and the Italian Football Federation tweeted their "profound condolences" to Astori's family as well as to the "directors, coaches and players who knew and respected Davide throughout Italian football."
The English Football Association announced that Astori will be honored in England's international friendly against Italy at Wembley Stadium later this month.
Former Italy team mate Andrea Pirlo was also left speechless by the news, writing: "In the end, the best always go first."
Beyond football's walls, former Italian Prime Minister Matteo Renzi, who was born and raised in Florence, was stunned and saddened by the news.
"It seems impossible. I'm in a state of disbelief and I cry with his family and all of Fiorentina. Goodbye Captain," he wrote on Twitter.
According to Italian media reports, Udine state magistrate De Nicolo said that Astori died of "natural causes" after a cardiac arrest.
The 31-year-old was married with a daughter and had made 289 appearances in Italy's top division.