The Moroccans died when their inflatable boat began to break up on Wednesday. The survivors were found clinging to the wreckage near the island of Gran Canaria by the crew of a Belgian ship.
"Those 11 human beings would have died if had not been for the professionalism, generosity and positive attitude of the ship's crew," Jose Segura, the Spanish government's representative in the Canary Islands, said.
A spokesman for the coastguard said the survivors – seven adults and four children - were in good health.
About 25,000 would-be migrants, about five times the number for all of 2005, have arrived in the Canary Islands this year. Most have made dangerous journeys of more than 1,000 km by sea from West Africa.
They usually arrive in open wooden boats with outboard motors and officials believe that many have drowned or died of thirst or exposure during the voyage.
More than 500 bodies have been recovered in waters between Africa and the Canary Islands this year but some non-governmental organisations have said the death toll could be as high as 3,000 people.
The upsurge in arrivals has made immigration one of Spain's biggest political issues and the government has put pressure on African countries to accept the return of as many of their citizens as possible.
European Union ministers - who have been divided over how to stop illegal immigration from Africa - agreed on Thursday to inform one another if they plan to grant mass amnesties to migrants.
The agreement is meant to prevent future disputes after Spain last year granted amnesty to some 600,000 illegal migrants without informing its EU partners.
Some EU nations have blamed the amnesty for the rise in African citizens landing illegally in the Canary Islands, Italy and Malta, saying it has made the area a magnet for migrants.
Officials said the measure, which will come into force at the end of this month, was urgently needed since a migrant who enters one EU country is able to freely travel to another EU nation.
The ministers are also expected to agree to speed up plans drafted by Franco Frattini, the EU justice and home affairs commissioner, to set up permanent "rapid border intervention teams" with boats and planes, as well as a Mediterranean coastal patrol network, using joint patrols to pick up migrants at sea.