WA police said that water police, police air wing, Surf Life Saving and the Surf Rescue helicopter responded to reports of a shark attack off Port Beach at 10.10am Saturday morning.
Water police were co-ordinating a marine search for the missing man, whose age had not yet been confirmed.
A spokesperson for St John's Ambulance WA said they had received a call at 10.03am of a shark bite and sent three crew to the scene.
Department of Primary Industries and Regional Development (DPIRD), Department of Transport (Marine) and Department of Transport (Marine) authorities also attended the scene.
Local councils have closed Port Beach and all beaches from Leighton Dog beach to Sand Tracks beach.
The ABC reported that, according to witnesses, the man was swimming next to a dinghy when a tiger shark and a great white shark attacked him. A group of boys who were in the dinghy say they saw the incident.
WA police acting inspector Emma Barnes said the search was ongoing.
Barnes added that "the actions of the witnesses were heroic and very brave".
"(They got) everyone else out of the water and notified everyone of what was happening," she said.
One man who was surfing at the time of the attack told the West Australian newspaper that a young teenager in a boat came "flying up in the beach" warning everyone.
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