The shark tore off the right-hand side of the boy's body in an off-limits section of water off the west coast of the island.
It was the 16th shark attack on the island since 2011 and the seventh death.
The boy, whose first name was given as Elio, was said to have been a keen and talented surfer.
Authorities immediately put in place a "post-attack procedure" in a bid to capture the shark.
A few hours after the attack a tiger shark measuring over 3.5 metres (11.4 feet) was captured and killed.
According to a medical examination of the boy's body, however, it was not the same shark.
Local police chief Dominique Sorain stressed that "engaging in swimming and water-based activities outside the protected zone is extremely dangerous."
"More than ever, we have to be doubly vigilant and the best way to prevent accidents is to respect the ban," added Sorain.
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.
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