The shark tore off the boy's limbs and part of his stomach as he was swimming in an off-limits section of the ocean off the west coast of the island.
It was the 16th shark attack on the island since 2011 and the seventh loss of life.
In February, island authorities extended until February 2016 a law prohibiting swimming and other water-based activities such as surfing and windsurfing except in special areas.
This measure has resulted in a dramatic decline in tourism and the cancellation of surfing and bodyboard competitions on the island, which lies to the east of Madagascar.
The waters off La Réunion are considered some of the deadliest in the world.
According to the International Business Times, locals suspect the rise in attacks is due to a marine reserve established in the area. Fishing has been banned there, which has allowed the marine ecosystem to grow and in turn has attracted predators, they say.