The body was recovered from the water after the attack, near Ethel Beach in the Innes National Park on the Yorke Peninsula, officers said.
A local resident told ABC News Thursday's attack was the first fatal one at the resort that he was aware of.
The attack is the latest of several in South Australian waters recently.
In a statement, South Australia Police said its officers were first alerted about the attack on Thursday at 13:30 local time (02:30 GMT).
"Sadly the body of a teenage boy was recovered from the water," police said in a statement.
The force, which did not give the age of the teenager, said officers were preparing a report for the coroner.
Ethel Beach is a 400m-long stretch of sandy surf beach, popular with surfers and tourists, with waves averaging 1.5 metres.
Local resident Marty Goody, who has been surfing in the area for decades, told ABC News that he estimated the victim may have been about "30 to 40 metres off the shore".
He said the area had always had sharks - "but there does seem to be a lot more of them now".
The shark attack is the latest of several in South Australian waters in recent months.
In May, a surfer was killed off the Eyre Peninsula, and in February, a girl was mauled by a shark in a river in Perth, the capital of Western Australia.
Australia has more shark attacks than any other country except the US.
Scientists have cautioned that an increase in shark sightings doesn't necessarily mean an increase in numbers.
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