The swimmer died from catastrophic injuries after being targeted by what witnesses said was a four-and-a-half metre great white shark at Little Bay in the city's east on Wednesday afternoon.
Randwick Council has shut a number of beaches including Little Bay, Malabar, Maroubra, Coogee, Clovelly and La Perouse for 24 hours.
"Council Lifeguards will patrol beaches over the next 24 hours looking for any further sightings of sharks," Mayor Dylan Parker tweeted.
"To lose someone on our coastline like this is chilling to the core," he told Sydney radio 2GB on Thursday.
"The coast is our backyard.
"Little Bay is normally a clam, quiet, family friendly beach."
NSW Ambulance inspector Lucky Phrachnanh said the swimmer "suffered catastrophic injuries as a result of the attack and there was nothing paramedics could do when we arrived on scene".
It is the first fatal shark attack in Sydney waters since 1963.
A witness told Nine News he saw a four-and-a-half metre great white shark attack the swimmer.
Kris Linto said the shark "attacked him vertically".
"We heard a yell ... it looked like a car had landed in the water," he said.
The unnamed victim is believe to be a local man who swam regularly in the area.
NSW Police and the Department of Primary Industry are investigating the circumstances surrounding the swimmer's death.
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