Some 52 others are being monitored, health officials say.
The nurse, identified in media reports as Teresa Romero, had treated two Spanish missionaries who died of Ebola after being repatriated.
Some 3,400 people have died in the current outbreak.
Most of the deaths have been in Guinea, Sierra Leone and Liberia.
The International Monetary Fund (IMF) has warned of the dire consequences for the economies in the region if the virus continues to spread.
Meanwhile the chairman of the World Health Organisation’s Ebola science group says he is not surprised that the Spanish nurse contracted the disease.
Speaking in Geneva, Prof Peter Piot said he expected more cases among medical staff, even in developed countries, and that the slightest mistake during the care of Ebola patients could be fatal.
Cleared
Reports said one of three people hospitalised in Madrid after the nurse’s diagnosis tested negative for the virus on Tuesday.
A female health worker, who also treated one of the Spanish priests, has been cleared in two separate tests, health sources say.
The husband of the afflicted nurse and a Spanish man who travelled to Spain from Nigeria remain in quarantine.
The European Commission has asked Spain to explain how Ms Romero, a 40-year-old auxiliary nurse, could have become infected. A hospital investigation is under way.
She was one of about 30 staff at the Carlos III hospital in Madrid who had been treating priests Manuel Garcia Viejo and Miguel Pajares, officials say.