The migrants risk sea voyages of up to 2,000 km (1,250 miles) from Mauritania, Morocco and Senegal in the hope of finding jobs or collecting welfare payments in Spain and elsewhere in Europe.
Migrant numbers have risen despite European Union sea and air patrols off the coast of West Africa.
In 2006 six times more illegal immigrants arrived in the Canary Islands than in 2005, Rodriguez said.
Tighter security on Morocco's borders has encouraged migrants to risk a sea journey that is quicker, cheaper and less arduous than overland routes to north Africa used previously.
People smugglers are also using bigger boats carrying up to 100 people and almost as many Africans landed on the Canaries this year as in the previous four years combined, Jose Segura, a government representative on the islands, told Cadena Ser.
In 2005, 4,751 migrants reached the Canaries. About 20,000 migrants have been transferred to mainland Spain this year from the islands, Segura said.
Spain's opposition Popular Party say that illegal immigrants are to blame for the recent rise in violent crime.
Polls show that Spaniards regard immigration as one of their biggest worries.