Police said the driver killed himself.
Broadcaster ZDF said police were searching his apartment and that he had contact with far-right extremists, but there was no evidence thus far that he was a far-right extremist himself.
Local media have described the 48-year-old as a psychologically instable man. The Interior Ministry in North Rhine-Westphalia, where Muenster is located, would neither confirm nor deny the Sueddeutsche report.
The paper reported that the suspect, who was not identified, had prepared extra-sharpened knives to use in the attack.
"The crime scene investigators are checking out the crime scene, trying to identify, investigate and secure traces. That is our current task", Mr Bode said.
News website Spiegel Online reported that Jens R. lived in Muenster and police had found an assault weapon at his flat.
A police spokeswoman said: "The danger is over".
"It's still unbelievable for me, but these days anything can happen", said Hubert Reckermann, a local man in his late 60s on Sunday.More news: David Warner accepts Cricket Australia sanctions over ball tampering
More news: Gender Pay Gap Deadline
More news: No mousing around as Disney offers to take Sky News
Police in the western German city of Muenster say a vehicle has crashed into a crowd there, killing several people and injuring others.
The Muenster University Hospital put out an urgent call for citizens to donate blood - and so many people rushed to help that long lines of donors formed.
German Chancellor Angela Merkel says she is "deeply shocked by the bad events in Muenster".
"Everything possible is now being done to clarify the facts and to support the victims and their relatives", she added.
While this incident is eerily reminiscent of three well-publicised terrorist attacks - the first at Nice in France in 2016, where dozens of people were killed when a lorry driven by Mohamed Lahouaiej-Bouhlel, a 31-year-old Tunisian man, ploughed into a large crowd watching a fireworks display to mark the Bastille Day holiday.
The presidents of Russian Federation and France, Vladimir Putin and Emmanuel Macron, as well as Spanish Prime Minister Mariano Rajoy sent their condolences.
On Saturday evening, the White House issued a statement sending US President Donald Trump's "thoughts and prayers" to the families of those killed. In the months prior to the Berlin assault, Germany suffered a number of small-scale Islamist militant attacks, which some linked to Merkel's decision in 2015 to open the country's borders to an influx of migrants, many of them refugees from conflicts in the Middle East.
The man who drove a van into a crowd in the German city of Munster was well-known to police and had a history of run-ins with the law, German prosecutors said, adding that they believe he acted alone.