The Department of Primary Industries and Regional Development said it was working with local authorities.
The man was brought to shore at Cable Beach in Broome. Photo / News Corp Australia
It is the second shark attack in Australia this week.
Mark Sanguinetti, 59, was surfing when he was killed by a 4.5m white shark at Tuncurry Beach, near Forster on the NSW mid-north coast, on Tuesday morning.
He saw the shark and tried to warn others before the animal turned on him, biting him on the upper right thigh.
Charlie Cernoboriwas, 58, was killed by a bull shark at Cable Beach while bodyboarding in November.
He was bitten on the upper thigh and hand.
That fatal attack was the first at the famous beach in almost three decades.