The 25-year-old Morosini, a midfielder for Livorno, collapsed after a cardiac arrest in the 31st minute at Pescara in central Italy. He never regained consciousness.
After the news of his death, Italy's football federation postponed all the weekend's professional matches. No date to play the Serie A games has been set although a midweek programme at some point in the next two months is likely.
Pescara prosecutor Valentina D'Agostino is also investigating to see if the delay may have cost Morosini his life. Doctors who were on the scene suggested that three minutes time probably would not have changed the tragic outcome.
"Everything that could be done was done," Ernesto Sabatini, one of the doctors who treated Morosini, told Ansa news agency.
"I was one of the first on the pitch and when I got to him he was already stiff."
Doctors said that Morosini's heart had stopped when he was on the field but an official autopsy is to be carried out on Monday to determine cause of death.
Piero Gnudi, Italy's minister for sport and tourism, told state television late on Saturday that he would see whether sophisticated medical equipment, including defibrillators, should be readily available at all professional sporting events.
Hundreds of Livorno fans visited the stadium on Sunday and left flowers and team scarves under a banner that read: "You fought right up until the end, goodbye great Moro." Many said Livorno should retire his number 25 jersey.
Morosini's girlfriend arrived in Pescara on Saturday to identify the body for legal purposes.
"He was smiling slightly. He was beautiful," she told her friends afterwards before breaking into tears, Ansa reported.
Morosini had also played for Udinese among other Italian club sides and Italy's international under-21 team.
