The man, who has not been named, was practising Downwind foiling some two miles west of Fuerteventura.
Spanish TV channel Antena 3 reported that he was in the water when the shark attacked his board and bit him on the leg on Sunday.
The media outlet published a video showing two bloody gashes just below the knee.
The wounds were described as 'deep' and panicked witnesses.
The man was seemingly able to fight off the shark and scramble back to the shore in the area of Los Molinos, a small hamlet to the west.
Sharks have been spotted before off Fuerteventura, and beaches have had to be closed when jet ski patrols raised the alert over the sea creatures near the shore.

The woman, who was said to be a crew member aboard the British-flagged catamaran, died after going for a dip in the sea.
She was rushed to a hospital by Spanish Air Force helicopter following the attack, which took place 278 miles south-west of Gran Canaria's airport.
However, the woman was pronounced dead after being evacuated to nearby Doctor Negrin Hospital, located in the Gran Canarian capital of Las Palmas.
Since records began, there have been only seven recorded instances of shark attacks on humans in the Canary Islands.
None of them have been fatal.




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