Despite his ordeal, the surfer, who is in his 40s but whose name has not been made public, managed to swim to the beach where rescuers took care of him.
Officials confirmed that he had suffered “serious injuries to his right foot and hand” but said that his life was not in danger.
The incident took place an hour and a half before sunset.
Experts advise against swimming in shark-infested waters at dawn and sunset when many sharks feed.
Sharks are not generally keen on eating humans, preferring less bony food, such as fish or seals, and most attacks appear to be mistakes.
But Réunion has experienced eight in the last 20 months, three of them fatal, and three attacks this year.
The last death was on 23 July when a shark bit off the leg of a 22-year-old surfer.
The mayor of the Réunion town of Saint Leu, Thierry Robert, who is also an MP, described the latest attack as “predictable”, pointing out that “once again” it took place in a marine nature reserve set up five years ago to safeguard coral reefs.
The reserve’s critics claim it is a “larder” for sharks, an accusation that its supporters deny, while environmentalists say that sharks have been attracted nearer to land by the dumping of human waste in the sea.
Last week Robert authorised shark fishing before withdrawing the decree because of a government promise that the state would move sharks from the area.
In a statement following Sunday's attack, he called on the government to take "the necessary measures to guarantee the safety of people using the reserve" and the surrounding area, "given that it considers itself the only competent authority" to do so.