The incident comes on a day of national mourning in Armenia for the 113 victims in a May 3 crash involving another Armavia plane.
That accident occurred as an Armavia Airbus 320 was preparing to land on the Russian Black Sea resort of Sochi.
In today's incident, four Brussels airport employees were injured, one seriously.
The fire broke out around midnight in a maintenance hangar and took two hours to quell.
Karla Daniels, a spokeswoman for the aircraft maintenance company Sabena Technics, said all four planes were "destroyed."
The other planes involved belonged to the Belgian military, the Greek carrier Hellas Jet, and Air Arabia, a low-cost airline operating out of the United Arab Emirates.