The state Fisheries Department immediately closed beaches in the area, which is the state's premier surfing and wine-making region, located south of the state capital, Perth. The victim lived in Margaret River, the main town in the region.
Marine officers were being sent with shark catching gear to deploy in the surrounding waters as soon as possible, the department said.
No details about the type of shark were immediately released, although great whites are often responsible for fatalities off the west coast.
The fatality is the first this year in Australian waters, where shark deaths average more than one a year and are becoming increasingly common.
After a spate of five fatalities off the west coast within 12 months scared tourists and locals alike, the Western Australia government last year approved a plan to kill sharks that venture too close to people in the water.
The policy infuriated conservationists and marked a sharp reversal of the previous policy, which permitted the killing of sharks only after they attacked.
There have been several shark attacks in Australian waters recently that did not end in death.
Greg Pickering, a 55-year-old abalone diver, was attacked around the head and back last month by what officials suspect was a 3-meter (10-foot) great white shark near the Western Australia city of Esperance, southeast of Perth. It was the second time Pickering had found himself in the jaws of a shark in nine years. In 2004, he was bitten on the leg while spearfishing near Cervantes, north of Perth.
-AP
