The attack also badly injured the 26-year-old male Costa Rican diving guide leading the group that included the American woman.
The shark savaged the two on Thursday as they were surfacing after a dive off Coco Island, a pristine national park located 500 kilometres off the Costa Rican mainland, the environment ministry said in a statement.
It stressed the attack was "an isolated incident" and the first one of such seriousness recorded for the island.
But as they surfaced, the shark went for the American woman, tearing at her legs.
The guide, too, suffered leg injuries.
Park rangers came to assist, as did doctors who happened to be diving in the area and who declared the woman dead.
The injured guide was taken to a hospital, where he was in stable condition and conscious. He told La Nacion he believed the shark was a female.
Tiger sharks, which have dark stripes on their body when young, are predators often found around Pacific islands. Unlike many other species of shark, they can be aggressive and account for a large proportion of reported attacks on humans.
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