"Police checks of the vehicle have been completed, no dangerous objects were found. Hanover airport resumed operations at about 20:05 (1905 GMT)," Hanover police tweeted.
They said earlier that the man drove onto the apron area at about 3.40pm.
The Hannoversche Allgemeine newspaper reported that the man, who was in his mid-20s, was under the influence of drugs and was driving a silver BMW with Polish licence plates.
He drove through the perimeter fence and tried to pursue an Aegean Airlines plane that had just landed from Athens, the paper added. Police stopped him after several hundred metres, it said.