The man has been identified by multiple outlets as 35-year-old Wolli Creek man and "keen diver" Simon Nellist.

He died from catastrophic injuries after being attacked by what witnesses say was a four-and-a-half metre great white shark at Little Bay.

NSW Premier Dominic Perrottet labelled it a "horrific tragedy" on Thursday, saying the government extended its sympathies to the family of the man.

"It's a reminder to us all of the fragility of life," the premier said.

"Can I also say to people right across our state we've closed a number of beaches on the advice of the Department of Primary Industries and police, so please follow those instructions."

The fatal shark attack is the first in Sydney in nearly 60 years.

Police confirmed to AAP they used DNA technology to identify the victim.

Randwick Council has shut a number of beaches including Little Bay, Malabar, Maroubra, Coogee, Clovelly and La Perouse for 24 hours.

"Our entire community is thinking of the family and friends of the victim today," said Randwick Mayor Dylan Parker in a council statement.

"This is a shocking tragedy that our area will feel for a long time."

The council said another assessment will take place on Thursday afternoon to determine if it will reopen on Friday.

But that did not deter members of the public from having a dip at nearby Clovelly beach in defiance of council's instructions.

Lifeguards surveyed beaches on jet skis and used drones to check for shark sightings along the coast.

Department of Primary Industries have installed six SMART drumlines between Little Bay and Malabar as part of a shark incident response plan, council said.

SMART drumlines are new technology that allow target sharks to be intercepted beyond the surf break.

Sydney University academic Chris Pepin-Neff, who focuses on policy responses to shark attacks, said "this was not a typical event".

He supported the authorities' decision to close nearby beaches.

"While killing individual sharks does not reduce the risk from shark bites, public education to stay out of the water when sharks are close to shore makes a difference," he said.

A local ocean swim planned for Sunday was cancelled "out of respect for the swimmer and his family".

Australian Associated Press