Flights have been delayed and diverted and passengers evacuated from the airport, while emergency crews were working on tackling the blaze.
The cause of the fire, which began at approximately 13:30pm local time, is not yet known.
There have been no flight cancellations yet, only delays, but plumes of thick black smoke may cause issues for several hours.
After nearly an hour at the scene, Aena confirmed that firefighters had brought the blaze under control and the area is being ventilated. There were no immediate reports of injuries or fatalities in the fire.