Jana Lutteropp was in very critical condition, Maui Memorial Medical Center spokeswoman Carol Clark said. Lutteropp's family requested that people respect their privacy during this difficult time, Clark said.
Lutteropp, 20, was snorkeling 50 to 100 yards off Palauea Beach in Makena on Wednesday afternoon when the shark bit off her right arm.
A California high school teacher swam out to bring her to shore after he and other bystanders heard her scream. Her arm wasn't recovered.
It's not known what type of shark bit Lutteropp. State officials investigating the attack said witnesses didn't see the animal.
On Sunday, a 16-year-old surfer suffered injuries on both legs after a shark bit him southeast of Hilo. He was airlifted to Hilo Medical Center.
The Hawaii Department of Land and Natural Resources closed ocean waters along the Pohoiki coastline after the attack.
Earlier Sunday, officials closed Hapuna Beach on the Big Island's northwestern shore after lifeguards spotted a shark.