The 46-year-old Elliston man was surfing at Walkers Rock Beach, about 365 kilometres west of Adelaide, when he was attacked on Saturday morning.
The man has been identified in media reports as local teacher Simon Baccanello.
No one else was injured in the incident, which was witnessed by multiple surfers.
Police, State Emergency Service and local community members spent the day searching for the man but were unable to locate him.
The search is continuing on Sunday with reports the man's surfboard has been found.
Superintendent Paul Bahr acknowledged it was a difficult time for the tight knit community.
"People are going to be in distress," he told reporters on Sunday.
"It will take time to get them to a point where we can talk to them and get statements from them.
"They would all know someone who was involved, if not the victim themselves, so I imagine it is very tough for them."
The incident occurred near a reef break popular with surfers in an area with a history of shark attacks.
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