The incident prompted a complete shutdown of the airport, with the secure areas being evacuated. The airport is located in Langenhagen, seven miles north of downtown Hannover.
A Hanover police spokesperson told DW that the man in his mid-20s drove out onto the runway and followed a plane from Greece's Aegean Airlines after it had landed. A quick test showed blood levels of cocaine and amphetamine.
No one was hurt, Hannover police said.
On Twitter the International Flight Network posted: 'Hannover Airport (HAJ) has now halted operations. Incoming and outgoing flights have been suspended until 8 p.m, although the airport terminal remains open.
Air traffic at the airport was paralyzed for more than four hours.
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All flights have been suspended after the incident happened at 3.40 local time on Saturday.
Officials have not said whether they're treating the incident as terror related. They said that "delays are high" and that a "Zero rate [was] applied for arrivals and departures due to an ongoing security issue on the airfield".
Bomb disposal experts were sent in to examine the auto and no risky objects were found. This is commonplace following such an incident.
The Hannover Airport has been put on a lockdown by Germany police after a man rammed through a gate in a vehicle and drove on the tarmac. The security areas are now vacated, now there is no clearance.
It wasn't immediately clear how long flight operations would be suspended.