One man was killed and two other people were hurt in the incident.
The attacker got out of his car armed with a knife. He was shot, injured and arrested by police.
He is being held on suspicion of murder and attempted murder, but police say there is no evidence of terrorism.
The attacker, described by police as being "without a migration background", drove what is thought to be a rental car into pedestrians in one of the city's central squares, injuring three people.
One of them, a 73-year-old German man, later died in hospital.
The attacker then left the car but was tracked down, shot and seriously injured by police.
He was questioned on Sunday in hospital after undergoing surgery but did not comment on the accusations against him, officials said.
The two injured people were a 32-year-old Austrian national and a 29-year-old Bosnian woman, police said. Their injuries were said to be minor.
An attack in December by a Tunisian Islamist who drove a lorry into a Berlin Christmas market, killing 12 people and injuring 49, has heightened security fears in Germany.
Investigators are trying to establish the motives of a 35-year-old German man who drove a car into a group of pedestrians in the city of Heidelberg on Saturday.