The man was taken to hospital after the encounter at Wylie Bay, east of the town of Esperance, Western Australia police told AFP.
He was believed to have lost one arm as well as his second hand and also suffered cuts to his leg, local newspaper The Esperance Express reported.
"It has been confirmed that at about 11 o'clock this morning, a man suffered serious injuries after being bitten by a shark -- unknown species -- at Wylie Bay," the WA Department of Fisheries said in a statement.
The department urged people to "stay out of the water", adding that beaches in the area were closed following the attack.
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Almost one year ago, 55-year-old commercial diver Greg Pickering survived a shark attack off Poison Creek beach, also east of the town of Esperance, despite suffering "substantial injuries".
The latest attack came weeks after the Western Australia government said it would abandon its controversial catch-and-kill shark policy after objections from the state's environmental agency.
The policy, which would have seen the use of drum lines to hook sharks off WA's busiest beaches during the southern summer, was introduced as a trial in late 2013 around popular west coast beaches following a spate of fatal attacks.
The last fatal shark was in early September at Byron Bay on the New South Wales coast, a popular tourist destination, when a man was killed after being bitten on the leg while swimming.