A woman is in critical condition after a shark attack at Coogee Beach on Saturday.

A woman, aged 35, sustained critical injuries to her left lower leg and arms after being bitten by a shark at Coogee Beach.

Emergency services were called to the beach in Sydney's eastern suburbs just before 11am on Saturday.

A local told the ABC they heard a "really chilling scream going out across the beach".

A woman is in a critical condition after being bitten by a shark at a beach in Sydney's east.