The motorist stopped the BMW underneath the wing of an A320 aircraft on the tarmac before being “overpowered” by police officers at around 3.40pm on Saturday.
All flights were suspended for more than four hours while German federal police investigated the incident and searched the car.
The 21 year-old driver from Poland was held on suspicion of dangerous interference with air traffic and resisting arrest.
Federal police later released a statement saying there were “currently no indications of a terrorist background” and that the suspect had tested positive for drugs.
It is believed the Aegean Airlines plane had just arrived from Athens.
“This afternoon a man with a BMW has passed through a previously closed gate on the grounds of the airport Hannover-Langenhagen,” the force said.
“A patrol of the Federal Police immediately took up the pursuit of the vehicle and followed the young man on to the [tarmac] apron.
“Here, the BMW stopped below the plane, a Greek airline Airbus 320 occupied by 172 passengers, and federal police officers overwhelmed the driver in his car.
“For security reasons, the air traffic was stopped immediately, the handling of all machines was interrupted and the security areas cleared.”
Police said no explosives or any other dangerous items were found during a search of the car.
“By his own admission, the person arrested is a 21-year-old man from Poland,” the police said.
“The investigation into his identity continues. A rapid drug test showed initial indications of anaesthetic effects.
“According to previous investigations, the man has no permanent residence in the federal territory.”
The suspect could appear before a judge on Sunday.
Hannover airport, the ninth-largest in Germany, reopened at around 8pm local time and passengers were asked to contact their airlines for information about their flights.
Join our new commenting forum
Join thought-provoking conversations, follow other Independent readers and see their replies