The incident occurred late on Monday when the Salvamento Maritimo rescue service was tipped off about a boat in difficulty 76 nautical miles south of Gran Canaria, one of the Atlantic archipelago's seven islands.
A Salvamento Maritimo spokeswoman said they had found two bodies on the boat, adding "four people were urgently evacuated" by helicopter to a hospital on Gran Canaria.
Another 34 people were pulled to safety, among them 27 men and six women, who arrived at Gran Canaria's Arguineguin port at dawn, the spokeswoman said.
In a post on X, formerly Twitter, the 112 emergency services said the four who were evacuated were in "serious condition" and that they had sent a large team to the port to treat the survivors.
The EU border agency Frontex says the Atlantic route to the Canary Islands is the busiest route for irregular migration from West Africa into the European Union.
The number of migrants boarding boats to attempt the crossing to the Canary Islands has risen more than six-fold so far this year from the same period of 2023, Spanish Interior Ministry data showed.
A total of 11,932 irregular migrants reached the Atlantic Ocean archipelago between January 1 and February 29, compared with the 1,865 who arrived in the same period in 2023, the ministry said.
The route has grown in popularity due to increased vigilance in the Mediterranean, with migrants fleeing poverty and conflict in Africa. Many boats — often long wooden fishing vessels known as pirogues — leave ports in Morocco, Western Sahara or Mauritania.
There has also been an increase in migrants from Gambia and Senegal.
Information for this article was sourced from Reuters and Agence France-Presse.