"During routine patrols, a dog detected explosives. An explosive detection device also reacted (positively)," border police chief Antonio Angelov told journalists at the airport.
"No device was found so far. The checks are ongoing," he added.
Bomb specialists using a robot blew open the doors of the vehicle parked outside one of the airport terminals and carried out a controlled explosion on one of the bags inside.
Police said the driver, a foreigner, parked the white Mercedes Vito outside at around 1:00 am (2300 GMT) and took a flight around 5:00 am (0300 GMT).
A bomb at Bulgaria's Burgas airport on the Black Sea in 2012 killed five Israeli tourists, the driver of their bus and the bomber.