A teenage girl from France was killed in a shark attack while swimming off the Indian Ocean island of Reunion, the fifth person to be killed by sharks on the island since 2011.

Local officials said the 15-year-old was attacked in the mid-afternoon while swimming just five metres from shore in the shallows of Saint-Paul bay on the western side of the island.

The teenager's body was sliced in two at the torso, and then "a part of her body was taken away by the shark", said Gina Hoarau, the head of public safety on the island.

The girl, who was named only as "Sarah" by French media, was swimming with another girl her age when the attack - just metres from a popular restaurant - happened.

The other girl had just climbed on shore when the shark struck.

"The conditions of this attack are very surprising. We didn't think a shark could come so close to the shore,'' said Ms Hoarau.

The girl, who lived with her mother in France, was on vacation with her father, head of a yacht club in St. Paul.