reported.
A small species of blue shark around 60-70cm long is thought to have attacked her, Mayor Alós added.
Beachgoers were told to avoid the area where the girl was bitten, but a full evacuation was not ordered because witnesses had not spotted the creature.
It is the first reported shark attack in the area in at least ten years, officials said.
But maritime experts said: "There is still the possibility that this was a normally harmless animal that confused the girl with prey".
Tourists in Majorca were placed on shark alert in May after pictures were taken of a mystery creature in the sea off Palmanova.
Holidaymakers stopped to take snaps of the monster fish – either a shark or a harmless red tuna – after it was spotted close to the party resort of Magaluf.
The sighting coincided with the busy Bank Holiday weekend and the first major influx of tourists to the holiday island after Easter.
Around 90 species of shark can be found in the Spanish Med.
Shark attacks in the sea, where the most common danger to bathers are jellyfish, are extremely rare.
A Spanish windsurfer was bitten in the leg in 1986 and seriously injured by what is thought to have been a Great White.
He later had to have a leg amputated. In 1993 a man lost several toes on one foot in a second attack by a two-metre long slender shark that was never properly identified.
A Great White shark was washed up injured at the Catalan resort of Tossa de Mar in 1992 and later died.
Authorities at the time were accused of covering up the incident through fear of upsetting the tourist trade.
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