A woman swimmer was seriously injured in a shark attack at a Sydney beach on Saturday, authorities said, in the latest of a spate of shark attacks off Australia's coast.

Suffering severe injuries to her limbs, the woman was airlifted to hospital for immediate treatment.

A woman in her 30s is being treated by NSW Ambulance after being bitten by a shark at the eastern suburbs beach.

A woman has been attacked by a shark at Sydney's popular Coogee Beach.