Jana Lutteropp, 20, had her right arm bitten off by a shark while snorkeling about 50 yards off Maui Aug. 14, the Honolulu Star-Advertiser reported.
"Jana fought hard to stay alive," Lutteropp's mother, Jutta Lutteropp, and sister, Julia Broeske, said in a statement released by Maui Memorial Medical Center where Jana had been on life support.
"However, we are sad to say that she lost her fight today. Jana was a very beautiful, strong, young woman who was always laughing, and we will forever remember her that way.
"We appreciate all the support from the Maui community, as well as the prayers and thoughts from around the world and in Germany."
The newspaper said a state database shows there have been eight shark attacks in Hawaii so far this year and 11 in 2012, but there had not been a fatal one in the state since 2004.