The driver shot and killed himself, a police spokeswoman said.
Authorities are treating the incident as a deliberate attack, the spokeswoman said.
Muenster police spokesman Andreas Boden told local media that the motive and identity of the driver is unknown.
The vehicle drove into a restaurant’s open terrace around 3:30 p.m. local time, according to police spokeswoman Vanessa Arlt.
Arlt said the old city remains closed, and police have asked people to avoid the city center.
Muenster, with about 300,000 people, is home to numerous universities and has a student population of about 58,000, the city government says. The city calls itself the cycling capital of Germany and says about 100,000 residents use a bike daily.
Ulrike Demmer, a spokeswoman for the German government, called news of the attack “horrible” on Twitter. “Our thoughts are with the victims and their loved ones,” she said.