The nurse had treated two Spanish missionaries who died of the disease after being flown home from the region.
Meanwhile, US President Barack Obama has announced plans to screen passengers flying to the United States.
Some 3,400 people have died in the outbreak - mostly in West Africa.
The Spanish auxiliary nurse, a 40-year-old woman whose identity has not been revealed, was one of some 30 staff at the Carlos III hospital in Madrid who had been treating Spanish priests Manuel Garcia Viejo and Miguel Pajares, officials say.
Mr Garcia Viejo, 69, died at the hospital on 25 September after catching Ebola in Sierra Leone.