The incident happened while the Pennsylvanian woman, 58, was on a trip at Green Cay, which is close to Nassau.
Police later said that the family identified the shark as a bull shark. A similar incident in the area took the life of a 21-year-old American in 2019.
Despite gripping public attention, shark attacks are exceedingly rare.
Bahamian police spokeswoman Chrislyn Skippings told reporters that the woman was on an excursion with a local tour company, which took her to the popular snorkelling area.
Family members and tour company staff saw her being attacked and managed to pull her from the water. A local news outlet, Eyewitness News, quoted Ms Skippings as saying that the victim suffered wounds to her “upper extremities”.
Her cruise ship, the Harmony of the Seas, was docked in Nassau at the time of the attack. It had just begun its seven-day cruise of the western Caribbean from Port Canaveral in Florida on 4 September.
Cruise operator Royal Caribbean International said in a statement that they are “providing support and assistance to the guest’s loved ones during this difficult time.”
The incident is the first fatal shark attack in the Bahamas since 2019, when a 21-year-old woman from California was attacked by sharks near Rose Island, about half a mile (0.8km) away from Tuesday’s attack.
In another recent incident, an eight-year-old British boy was injured after being attacked by three sharks in another part of the Bahamas. His father later told The Sun that the attack “was like a scene out of Jaws”.
In total, statistics from the Florida-based International Shark Attack File show that only about 32 shark attacks have been reported in the Bahamas since 1749, the highest number in the region.
Globally, there were 73 confirmed unprovoked shark attacks in 2021, including nine which resulted in death.