A cruise passenger has been killed in a shark attack while swimming with her family in the Bahamas, according to local police.

The 58-year-old woman from Pennsylvania was snorkelling off the coast of Rose Island, Nassau as part of a Caribbean cruise holiday when the incident took place.

Shortly before 3pm local time she appeared to be in trouble. The police report that the family saw a bull shark attack her, causing injuries to her left side. Tour operators and family members attempted to help the woman but were unable to save her. She was transported to New Providence island, where she was pronounced dead on arrival.

ABC News identified the victim as Caroline DiPlacido of Lake Erie. She had arrived on the island earlier that morning, Tuesday, as part of a Royal Caribbean Cruise itinerary.

She had departed Florida on Sunday Night on Harmony of the Seas, three days into a seven-night cruise with her family.

Police spokesperson Chrislyn Skipping told media that the woman was taking part in a shore excursion with a local snorkelling company, in an area popular with cruise tourists.

Cruise owners Royal Caribbean International released a statement on Tuesday saying they were "providing support and assistance to the guest's loved ones during this difficult time."

A similar incident took place at the beach in 2019, when a 21-year-old American tourist was killed by a shark. This took place less than a kilometre from Tuesday's attack.

Despite the intense public attention, local authorities said that shark attacks are extremely rare.

A Florida-based shark attack database, the Shark Attack File reported that the Bahamas accounted for the highest number of shark attacks in the region - although this was only 32 attacks in the last 270 years.

Michael Heithaus, a marine biologist at Florida International University, told the Associated press that the Bahamas accounted for a disproportionate number of shark attacks due to the high number of tourists in the water.

Last year there were 73 confirmed unprovoked shark attacks globally, nine of which were fatal.