Emergency crews are working to extinguish the blaze and find out how much damage has been done to other planes involved in the Nato exercise, the ministry said in a statement.
A Nato spokeswoman talking to the AP news agency declined to reveal details of the accident.
Spanish officials said that the jet was participating in a Nato training exercise called the Tactical Leadership Programme (TLP).
The TLP is not part of the Nato structure but is an organisation formed under an agreement between 10 Nato nations whose aim is to increase the effectiveness of allied air forces through the development of leadership skills.