According to police, the fire also affected three civilian cars that were completely destroyed, German magazine Spiegel Online reported.
The German police have started their investigation, but it still remains unclear who was behind the attack. According to the magazine, the possibility of political motives behind the crime cannot be ruled out.
Another incident of that kind took place on New Year's morning in Leipzig, where eight official customs vehicles were set on fire.
A spokesman of the Bundeswehr in Dresden said that the amount of property damage in the recent incident is unknown. The vehicles are currently undergoing inspection.