The incident occurred near a beach about 350 kilometers north of Sydney in the state of New South Wales. Another person, a man, was injured in the leg in the attack.
They knew each other, and were out swimming when the shark attacked, says Timothy Bayly of the police.
The beach and surrounding area have been closed and authorities are working to determine what species of shark attacked the two swimmers.
The area is so remote that there are no lifesaving services there at all, Steven Pearce, head of the organization Surf Life Saving NSW, told a local radio station.
As recently as September, another fatal shark attack occurred in the state, when a surfer lost his life off Sydney.
