The victim was snorkeling near the beach of Linderalique at Hienghene, a village located to the north-east of the archipelago.
Firefighters said friends dragged him ashore and applied a tourniquet.
The Noumea resident was taken to hospital where he was operated on.
The species of shark responsible for the attack has still not been determined. Hienghene authorities moved to ban bathing on the beach, which is located near a resort.
On December 16, bathing was temporarily halted at the popular Lemon Bay beach in Noumea due to the presence of a shark about three metres from the shore.
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