The beach has since closed, according to the Associated Press.
Mr Medici, who is the first man to be killed in the state in more than 80 years, came to America for college two years ago.
Witnesses say the man was boogie boarding with a friend when the shark aggressively attacked.
Then the victim's friend dragged him to shore.
Newcomb Hollow Beach in Wellfleet, MA. appears in this undated stock photo.
'It was like right out of that movie Jaws. "This has turned into Amity Island real quick out here", he admitted to WBUR.
Life-saving measures were attempted on the beach before the man was taken to Cape Cod Hospital in Hyannis, where he was pronounced dead, State Police spokesman David Procopio said.
A 61-year-old NY neurologist was bitten by a great white shark August 15 at Long Nook Beach in Truro.
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Sightings of great white sharks have soared this year in Cape Cod, where the suspected shark attack happened.
Visitors to Newcomb Hollow Beach are greeted by a sign warning them to "Be Shark Smart".
Hurley said the Cape Cod District Attorney will handle an investigation in to the incident.
"We are witnessing sharks feeding aggressively in shockingly shallow water on an nearly daily basis over this past August", he wrote.
Hayley Williamson, a Cape Cod resident and former lifeguard who was on the beach at the time, was left in disbelief.
Reinhart said she hoped to discuss the incident with fellow Select Board members before saying anything further.
The agency said it would continue to work with the Atlantic White Shark Conservancy, the Cape Cod National Seashore and others to provide information to help swimmers stay safe. "Right spot, wrong time, I guess".
He sustained severe injuries to his legs and is still recovering in hospital.