Maria Teresa Romero Ramos, 40, is the first person known to have contracted the deadly virus outside West Africa.
She had treated two Spanish missionaries who later died from Ebola.
A World Health Organization (WHO) adviser has warned that more Ebola cases can be expected among medical staff, even in developed countries.
Teresa Romero remains in quarantine in the Spanish capital along with her husband and three other people.
A fifth person, said to be a friend and colleague of Teresa Romero, was admitted on Wednesday morning with a slight fever. In all, more than 50 people in Spain are under observation.
Teresa Romero was part of a team of about 30 staff at the Carlos III hospital in Madrid looking after the missionaries when they were repatriated from West Africa.
Miguel Pajares, 75, died on August 12 after contracting the virus in Liberia, while Manuel Garcia Viejo, 69, died on September 25 after catching the disease in Sierra Leone.
New figures released by the WHO show that more than 8,000 people have now been infected with the disease and 3,879 have died. The vast majority of deaths have been in Guinea, Sierra Leone and Liberia.
Teresa Romero told El Pais that she might have become infected when removing her protective suit after cleaning Manuel Garcia Viejo’s room.
“I think the error was the removal of the suit,” Teresa Romero told El Pais by phone.
“I can see the moment it may have happened, but I’m not sure about it.”
Teresa Romero added that she did not have a fever on October 8 and was “doing better”.
In another development, the woman’s husband, Javier Limon, is reported to be fighting a court order to have their pet dog put down over fears it could be carrying the disease. Animal rights groups have also criticized the move, saying there is no evidence Ebola has been spread by dogs.
Meanwhile, the head of Medecins Sans Frontieres (MSF) in Sierra Leone says the rest of the world is not doing enough to combat the outbreak of the Ebola virus.
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