Armin Trojer, 19, of Baden, Austria, was airlifted by helicopter to Lee Memorial Hospital in Fort Myers, where he was in good condition, hospital spokeswoman Pat Dolce said.
"It is a confirmed shark attack," said Lee County sheriff's spokeswoman Ileana LiMarzi. "Someone else in the water saw a shark."
The attack occurred near the lighthouse at Gasparilla Island Beach.
"We are out there right now letting people know, notifying people on the beach about what happened," LiMarzi said. The beach was not closed to swimmers.
Two other young people have been bitten since Saturday in gulf water off Florida. The latest incident was about 280 miles (450 kilometers) from an attack Monday on a 16-year-old boy who lost his leg and about 350 miles (560 kilometers) from the spot where a 14-year-old girl was killed Saturday.
Experts believed bull sharks attacked both teens in the Florida Panhandle. The type of shark involved in the Boca Grande attack was not immediately determined.
Experts say shark attacks are rare, pointing out that there were only 30 in 2003 among the millions of people who hit the state's beaches. Most of those attacks were minor bites on the feet or ankles.
Last year, when four hurricanes kept many visitors away, there were 12 attacks.