The boat was intercepted yesterday in the Atlantic some 18 nautical miles southeast of the island.
The group of 33 men, six women and the child were taken to the Gran Canaria port of Arguinequin, a local emergency services official said.
All were in good health although two passengers, a man and a woman, were taken to a medical centre to undergo checks for minor health ailments, he added.
Spain's Canary Islands off the coast of Morocco were a key route a decade ago for migrants from Africa trying to reach Europe, but their numbers fell after Spanish and African authorities increased patrolling.
The Spanish coast guard picked up 34 migrants on a boat off the Canary Islands in mid-July, another 32 in early August and about 40 in early September.
The crackdown on the Canary Island route has meant more traffic through the western Mediterranean, across the Strait of Gibraltar.
Spanish authorities saved some 3,500 migrants who arrived in the country by boat last year, a 55 percent increase over 2013.
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