Officials say a female diving guide was bitten on the thigh and buttocks by a shark but was saved when another swimmer pulled the shark's tail.
Frank Pisani of Fremantle Sea Rescue said on Sunday that an unidentified man grabbed the shark by the tail as it bit Elyse Frankcom in waters about 30 miles (50 kilometres) south of Perth.
Mr Pisani said Ms Frankcom started to sink to the bottom but the man grabbed hold of her and brought her to the surface and back on board the boat.
Ms Frankcom had been guiding a group of people on a dive with dolphins on Saturday.
Department of Fisheries spokesman Tony Cappelluti says the 10-foot (three-metre) shark was either a great white or a whaler shark.
Ms Frankcom is in stable condition after surgery on Sunday.