The Virgin Islands Police Department received an emergency call reporting the shark attack at 4:28 p.m. local time, and marine units and fire and emergency medical services personnel responded.
They found a woman who lost an arm in the attack and searched for a possible second victim, but found no one else.
The woman later was identified as Arlene Lillis, 56, of Minnesota, and she eventually died from her injuries.
"Our hearts are with the family and loved ones of the victim, and with everyone who witnessed this tragedy," Virgin Islands Gov. Albert Bryan Jr. said in a statement.
"We have been briefed on the information known at this time," Bryan said. "We are grateful to the bystanders who acted immediately to render aid and to the first responders who worked urgently and bravely in an effort to save her life."
The type of shark was not identified, and the attack remains under investigation.
It is the second fatal shark attack that was confirmed in the United States and its territories in recent weeks.
Erica Fox, 55, died when a shark attacked her in California's Monterey Bay in December.
She initially was reported missing, but her body eventually was found.
A coroner said Fox died from "sharp and blunt-force injuries and submersion in water due to a shark attack."
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