Local authorities are asking the rest of Spain and the European Union to help care for the children, the BBC reports.
More than 4,500 mainly African illegal immigrants landed on the Canary Islands this month -- nearly as much as normally arrive in a year.
All told, more than 18,000 illegal immigrants have arrived on the islands by boat so far this year.
Detention centers on the islands have a capacity for only about 5,500.
To cope with the overflow, the government has transferred thousands of immigrants to Spain's mainland, crowding Red Cross shelters in Madrid, the BBC said.
The Conservative Popular Party claims Spanish Prime Minister Jose Luis Rodríguez Zapatero is washing its hands of the immigration problem by sending most of the immigrants to regions administered by the opposition.
2014: The Year in Music [PHOTOS]