Hospital sources say the priest had been in Liberia and was in contact with people who were infected with the virus.
Ebola has killed almost 4,500 people as it spreads across large areas of West Africa.
The priest belongs to the same religious order as two other Spanish priests who were repatriated from Africa when they picked up the disease. They both died.
Spanish newspaper El Mundo says he is suffering from a fever of over 37.6 degrees Celsius.
Meanwhile, the European Union has promised to reinforce passenger screening for Ebola at airports.
The EU has also pledged to create a common approach to checking for the virus at airports in Europe.