Authorities will continue to patrol a popular swimming area in Perth's Swan River after a rare shark attack left a man in his 50s critically injured.

The man, identified by local media as Cameron Wrathall, suffered severe blood loss after he was bitten on the leg by a bull shark on Thursday morning at Blackwall Reach.

Mr Wrathall was assisted by kayakers before being rushed to Royal Perth Hospital and taken into surgery.

He remained in theatre on Thursday afternoon, where he was in a critical but stable condition.

Western Australia's fisheries department is investigating the attack - an unusual incident for the river - and said the shark was reported to be two to three metres long.

Overlooked by multi-million dollar riverside mansions, Blackwall Reach is known for its limestone cliffs and russia popular with kayakers and swimmers.

A water police vessel arrived on the scene after the attack and cleared swimmers from the water.

The City of Melville has closed a stretch of the river between Bicton Baths and Point Walter, while the Town of Mosman Park has closed the beach area at Chidley Point opposite Blackwall Reach.

Fisheries officers will continue water and land-based patrols throughout Thursday and Friday, while WA Police and Surf Live Saving WA helicopters have conducted aerial sweeps.

Premier Mark McGowan praised the efforts of kayakers to rescue the man while highlighting the rarity of such an attack.

“I understand it's quite a serious bite but we all hope and wish for the very best for the man involved and hope he recovers fully,” he told reporters.

“We haven't had an attack by a bull shark in the river for 50 years. The last time someone was killed by a bull shark in the river was 100 years ago. So this is unexpected and surprising.”