The accident occurred "owing to poor conditions at sea amid three-metre waves and winds gusting at 30 knots," the official said.
The capsized boat was a wooden craft known in Spain as a "cayuco". Often brightly painted, they are powered by outboard motors and their bare hulls offer little shelter to occupants who sometimes die of hypothermia.
"We're talking about a very fragile craft," said Joan Mesquida, the director general of the Spanish police, explaining how survivors were plucked from the sea.
Spanish authorities estimate 31,200 immigrants, mainly from sub-Sahara Africa, arrived in the Canary Islands last year more than three times the previous annual record.
More than 250 would-be immigrants have reached the islands since Sunday alone, with some 4,700 making it since January, despite tighter surveillance of the African coastline in recent months by the EU border patrol agency, Frontex.