Some 120 people were evacuated following the fire in Villajoyosa.
Fifteen lightly injured people were taken to hospital for treatment for smoke inhalation, police told AFP.
The fire, which started at around 2:15 am (0115 GMT) on the 11th floor of a 24-storey building, has been brought under control and the other residents were able to return to the building on Monday.
The blaze erupted less than two weeks after another fire killed 10 people in the port city of Valencia in the same region, in a tragedy that shocked the country.
The fire in Valencia devastated a 14-storey high-rise building and an adjoining 10-storey block which together housed 138 flats.
Experts said the building was covered with highly flammable cladding, which could account for the rapid spread of the blaze.
It prompted worried property owners to seek expert advice to ally fears that their own homes could be at risk.
Barely 10 days ago, at least four people died in a vast fire that ripped through a 14-storey apartment block in Valencia in eastern Spain, but officials warned Friday that the death toll could rise sharply.
Nineteen people were still missing, a city hall source told AFP on condition of anonymity.
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