Bethany Hamilton was attacked on Kauai's North Shore on Friday morning, authorities said. There was a single bite, and then the shark disappeared.
"There was no warning," said Battalion Chief Bob Kaden.
The teenager was surfing with her best friend and her friend's father, who immediately applied a tourniquet using a surf leash. Hamilton's mother, Cheri, said the move saved her life.
Tom Hamilton said his daughter was conscious and alert at a hospital. She lost her left arm just below the shoulder. Her arm had not been recovered.
The shark took 40-by-20 centimetre chunk out of the surfboard, suggesting the fish was 3.6 to 4.5 metres long, Kaden said.
It was the fourth shark attack this year in the area. Randy Honebrink, spokesman for the state Shark Task Force, said Hawaii averages three or four attacks annually.