Nat Drummond was about 700 metres off Seacliff beach on Sunday when the shark struck, ripping a large hole in his ski.
The impact hurled the 19-year-old backwards into the water. He was pulled to safety by other paddlers and returned to shore unhurt.
Surf Lifesaving SA emergency operations manager Daniel Willetts said the tooth and flesh recovered from the damaged ski was being examined by Flinders University's marine biology department to try to determine what species of shark was involved.
Mr Willetts said there had been no shark sightings in the area before the attack and none since.
"It was just an incident that occurred without any warning. We know that happens," he told reporters on Monday.
"We don't know whether that creature's still there, whether it's moved on or whether there's other creatures in the area."
The beach remained open after the attack but beachgoers were advised of the incident so they could make an informed decision on whether or not to enter the water.
Mr Willetts said there was no doubt Mr Drummond had a lucky escape but understood he was keen to get back to training and competing.
"We know that these things can happen. It's a risk we take when we enter the water," he said.
After the incident, Mr Drummond said the shark had struck from below and lifted him and his ski into the air.
"I saw the shark and it was pretty big," he said.
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