No one was hurt in the incident, but flights were suspended for more than four hours.
Police said a test suggested that the driver, who told them he was a 21-year-old from Poland, was under the influence of drugs and there were no indications that his actions were terror-related.
Takeoffs and landings were halted while police experts examined the car. They found no traces of explosives, and flight operations resumed shortly after 8 p.m. — about 4½ hours after the man drove onto the airfield. No other dangerous substances were found in the vehicle or on the driver.
The man was believed to have acted alone. He apparently has no official residence in Germany.
Federal police told the German news agency dpa that the driver tested positive for amphetamines and cocaine. They said the man wasn't carrying an identity card.
The police statement issued later Saturday said authorities had taken a blood sample and were still working to be certain of his identity.
Police opened an investigation on suspicion of dangerous interference in air traffic and resisting officers, and were considering whether to have the man taken before a judge Sunday to try to have him kept in custody. His motive remained unclear.
The international airport in Hannover handled 5.87 million passengers last year, though it isn't one of Germany's top hubs.