The boat was spotted by a merchant ship 140 km south of Gran Canaria on Monday evening.
Four people in critical condition were evacuated to a hospital aboard two helicopters, while 34 others were transported by boat to the port of Arguineguín, Spain’s maritime rescue service said. Among the survivors are seven women.
Spanish authorities are facing an influx of migrants and refugees from West Africa reaching the archipelago, a springboard to continental Europe.
Nearly 12,000 people fleeing poverty, conflict and instability in West Africa arrived in the Canaries in the first two months of the year, according to the Spanish Interior Ministry, more than six times the number recorded during the same period last year.
Most migrants set out from the Mauritanian coast on artisanal fishing boats called pirogues and navigate for several days against the strong winds and currents of the Atlantic. While thousands of people survived this risky journey, many died or disappeared along the way and the remains were sometimes washed across the Atlantic.
Last week, two canoes that had left Mauritania for Spain were found adrift hundreds of kilometers away, near the Cape Verde archipelago, after failing to reach their destination, according to the police.
Eleven survivors were rescued from one boat and five more from the second boat, but one person later died. Five bodies were also found and dozens more were believed to have been lost at sea.