A car is suspected of having rammed a fence at the airport, police said, according to the DPA news agency.
The damaged section of the fence is adjacent to several parked Russian cargo planes. A major police operation took place overnight, but no unauthorised people were found on the airport grounds.
One of the airport's two runways has been closed.
On August 4, a drone carrying explosives was discovered at the airport, near Ukrainian cargo planes. At the same time, a second drone collided with an aircraft in mid-air. Ten days later, a third drone was found near the airport, also carrying explosives.
The German government explicitly singled out Russia as responsible for plans to carry out sabotage.