A woman is recovering in hospital after being attacked by a juvenile great white shark near La Perouse in Sydney's south-east.

The woman, aged in her 50s, was swimming at Congwong Beach when the incident occurred shortly before 7:00pm last night.

The New South Wales' Department of Primary Industries' senior shark biologist, Vic Peddemors, said he had examined photographs of the woman's wound and determined a great white shark between 2.7 and 3.2 metres long was responsible.

Paramedics attended the scene and transported the woman to St George Hospital, where she had emergency surgery.

Mr Peddemors said the shark was a "juvenile" and the woman, who was bitten in the right lower leg, was in a stable condition.

Beachgoers at La Parouse watch as a helicopter searches for sharks after the attack there yesterday. ( ABC News: Sarah Hawke )

"[It's a] reasonably severe bite but fortunately she's stable and is undergoing surgery … I'd be surprised if she had any severe damage.

"Normally juvenile sharks feed on fish, but as they get larger they start including turtles and marine mammals like dolphins and seals in their diet," Mr Peddemors said.

"Obviously there's no mother to tell them what to eat and what not to eat so they are exploring whether … larger objects are edible."

He said there was no requirement "for shark nets to be put up … because of a single white."

'An unusual event'

Mr Peddemors said there had not been any shark attacks in the La Perouse area for "an extremely long period".

"This is an unusual event, shark bites as a whole are an unusual event," Mr Peddemors said.

Randwick Mayor Lindsay Shurey said the community was in shock following the attack.

"From all accounts the woman was very lucky and certainly the whole community's heartfelt thoughts are with her for a full recovery," Cr Shurey said.

"I've lived in the area for 25 years and this is the first confirmed shark attack in Randwick City. We're all a little shocked and concerned."

Beaches in the area remain closed.

Council lifeguards will be stationed at the usually unpatrolled beaches on Saturday.