Western Australia Premier Colin Barnett has said he would consider a shark cull, and his government is looking into the possibility of increasing aerial shark patrols.
But scientists have warned against over-reacting.
Barbara Weuringer, marine zoologist and shark researcher at the University of Western Australia, urged against a shark hunt, saying the only way to know which shark attacked is to kill one and open up its stomach.
"It sounds a little bit like taking revenge," she was quoted by AP as saying. "And we’re talking about an endangered species."
Sharks are a common feature of Australian waters but, according to the Australian Shark Attack File, attacks are rare with only 53 fatalities in the last half-century.