The driver, a 40-year-old German from the neighboring state of Rhineland-Palatinate, was also injured in the incident and is being treated in hospital, Baden-Württemberg Interior Minister Thomas Strobl told the dpa news agency.
The driver fled the scene after the incident but was captured by police and arrested after a short manhunt. No information has been released on whether the incident was premeditated.
German Interior Minister Nancy Faeser canceled her plans for Cologne’s Rose Monday parade and will visit Mannheim instead.
“Saving lives, caring for the injured and the initial investigation by the authorities in Mannheim are now our top priorities,” Faeser’s spokesperson said.
Following the incident, three people are currently being treated at the University Hospital in Mannheim and are receiving acute medical care, the hospital said.
Another major German city, Munich, was the scene of a car attack in mid-February when an Afghan asylum seeker drove into a trade union demonstration.