The man’s wife had called police about a possible child abduction, the force added.
Police said later that the 35-year-old man had a four-year-old child inside the car and that they assumed he was the father and had taken the child by force from the mother in a possible custody battle.
Federal police spokesman Thomas Gerbert told German news agency dpa that a large number of officers from state and federal police were on site and in the vicinity of the vehicle.
Police also said that a psychologist was talking with the man and that there was no indication other people could be harmed since all passengers had evacuated the airport.
All departures and arrivals at the airport have been halted.