A man's leg has been completely severed below the knee after he was attacked by a shark while surfing in the Hawaiian waters of Maui.

The 61-year-old man was surfing off Waiehu Beach Park on Friday morning when a shark bit him.

His right leg was "completely severed just below the knee," Maui County said in a statement.

The man was alert while being treated on shore and then taken to Maui Memorial Medical Centre in a critical condition.

Police officers had first tried to control the bleeding with tourniquets when they arrived at the scene.

The surfer did not see the shark approach, the authorities added.

Officials warned people to stay out of the water in the area and closed the beach park, with people being told to stay out of the water for a mile in each direction of the incident will be in effect until at least noon on Saturday local time.

The warning will be extended if there is a shark sighting in the area - and Maui fire and ocean safety officials were patrolling the waters using rescue watercraft and a drone.

There were no details provided on what kind of shark was involved.

The man's current condition is not known.

In June, Tamayo Perry, a lifeguard and surfing instructor who also appeared in a Pirates of the Caribbean film, was killed in a shark attack while surfing off Oahu in Hawaii.