One of the plane's engines caught fire at about 6.20 a:m (0320 GMT) as the plane was sitting on the runway waiting to fly to Budapest, Hungary, Alin Maghiar spokesman for the General Inspectorate for Emergency Situations was quoted as saying by state news agency Rompres.
Wizz Air said in a statement there was a problem with an engine but did not elaborate.
The fire was put out by the plane's internal extinguishing system, Maghiar said.
Some 25 firefighters at the airport helped the passengers evacuate, he added.
Passengers were waiting to be boarded on another plane, and the flight will be delayed by 11 hours, the company statement said.
Wizz Air apologized for the incident and reassured its customers of the safety of its flights.