The man, reported to be in his late 20s, was surfing off the small fishing town of Saint-Leu when the attack took place on Thursday.
The local government confirmed that a surfer had been killed as it called for vigilance in the sea.
Surfing and other water activities are heavily restricted on Réunion due to the high risk of shark attacks.
The attack took place at about 16:30 local time (12:30 GMT) off the coast of Saint-Leu, on the west of the island.
A witness alerted rescue officials, telling them a surfer had disappeared from the surface of the water and that only his board was visible from the shore, the local government said in a statement (in French).
It gave no details about the identity of the surfer.
Rescue officials told French media that the shark tore off one of the surfer's legs, and his body was later recovered from the port of Saint-Leu, where he was pronounced dead.
Three other people surfing with the man got back to shore safely, they said.
The incident reportedly took place in an area where surfing is prohibited.
Ahead of the attack, the local government had issued a statement (in French) on Thursday morning urging caution in the sea, citing the risk of bull shark attacks amid shifting temperatures.
Réunion has historically been a popular destination for surfers.
However, in recent years it has also become known as a shark attack hotspot and surfing there is widely restricted.
Following the latest incident, the local government said the strict measures were necessary to keep people safe.
Thursday marked the 24th shark attack and the 11th fatal one reported on the French island since 2011, according to reports.
Comment: Shark attacks are on the rise in the US and Australia