Authorities are hunting a shark that killed a 32-year-old American man at Rottnest Island, off the coast of Western Australia.

Police say the man, who had arrived in the state earlier this year for work, was diving and spear fishing on Saturday afternoon when it is believed he was attacked by the three-metre shark.

WA Premier Colin Barnett described the man's death as "tragic" and ordered that the shark responsible to be caught and killed.

"Within an hour of that situation occurring the Fisheries Minister [Norman Moore] and the State Government authorised that the shark be caught and destroyed, if possible, and the fisheries officers are now attempting to do that," he said.

The man's death off the island's Little Armstrong Bay is the second shark fatality in WA within two weeks, after 64-year-old Bryn Martin was killed at Perth's Cottesloe Beach on October 10.

Water Police Senior Sergeant Greg Trew said police received a call on Saturday afternoon that the shark victim had surfaced in "a flurry of bubbles".

He said the American citizen had "fairly horrific injuries" and was believed to be dead when he was pulled from the water by his diving companions.

The attack happened about one kilometre off the north of Rottnest, a popular holiday island near Perth, when the man was diving alone from a 25-metre vessel.

Senior Sergeant Trew said the shark was seen by the man's two companions as they were leaving the area after retrieving the body and they reported it to be three metres long.

"It's traumatic for everyone involved, it's a tragic situation," he said.

All beaches on Rottnest Island were closed on Saturday afternoon after the attack.

'Natural predators'

Mr Barnett said his government will review whether to increase the numbers of sharks that commercial fisherman were allowed to catch, following reports from fishermen that shark numbers had increased significantly.

"Sharks are natural predators, this is their domain. People are generally aware of the risk," he said.

He also said his government would look at increasing aerial shark patrols over popular WA beaches.

But the premier noted that the latest attack occurred well off the shore where no patrols would operate.

Perth resident Georgia Foulkes-Taylor is on the island to participate in a fun run. She says the news of the attack spread quickly.

"We heard a guy yelling get out 'get out of the water' and we didn't think much of it we kind of joked about 'oh there's a shark' but then my sister and her friend were pedalling close to where it happened and they came rushing back saying they'd they heard some guys talking about a shark attack," she said.

Police and the Department of Fisheries will investigate the attack and a report will be prepared for the coroner.

Saturday's attack was the fourth off the WA coast in 14 months.

Last month, 21-year-old body boarder Kyle Burden was killed near Bunker Bay in WA's south-west by a shark.

Just south of there in August last year, 31-year-old surfer Nicholas Edwards was killed by a shark at a surf break near Gracetown.

Sorry, this video has expired Watch 7.30's report, which aired on Friday, about shark attacks in WA

ABC/AAP