Paul Rolle, deputy commissioner for the Royal Bahamas Police Force, identified the victim as Jordan Lindsey of Torrance.
According to police, there were three sharks involved in the attack. They bit her in the arms, legs and buttocks, and severed her right arm, officials said.
Family members, including Lindsey's parents, were with her during the snorkeling expedition near Rose Island around 2 p.m.
Officials said family members saw the sharks and yelled a warning to her, but she didn't hear them in time.
She was brought to a local hospital where she was pronounced dead.
"Jordan was 21 and such a great daughter and person. We already miss her terribly," Jordan's father Michael Lindsey said in a statement to ABC News:
Lindsey was a student at Loyola Marymount University.
Officials with the Bahamas government said: "The Ministry of Tourism, on behalf of the Government and the people of The Bahamas expresses its condolences and deepest sympathies to the family and loved ones of the victim of Wednesday's shark attack off Rose Island, near New Providence."
The U.S. Embassy is working to bring her body back to California.
ABC News contributed to this report.