Christine Armstrong, 63, was attacked as she attempted to swim the 1970ft between a wharf and beach near the village of Tathra, 210 miles south of Sydney.
Local council official Leanne Barnes said the victim was part of a group of locals who meet at the beach every morning to swim out to the wharf and back.
The Tathra Wharf to Waves - a swim from the wharf to the beach and back again - is an annual event that attracts hundreds of swimmers each summer.
Ms Armstrong's family said she had been swimming at the beach for 14 years and had been a trainer at the local volunteer lifeguard club.
In a statement, they said: "Swimming brought her much joy and many friends. She will be sadly missed by all who loved her, especially by Rob, her husband of 44 years."
Police said a helicopter and boat were being used to search for remains.
No details on the species of shark were released, but fatal attacks are becoming more common in Australia.