A security source added: "The scenario is such that an attack can not be ruled out". Police quickly set up a large cordoned-off area for their investigation and ambulances rushed to the site. The perpetrator killed himself upon performing the attack.
Mr Reuel also said that two people had been killed by the driver, revising an earlier police figure of three.
"We now know it was in all likelihood a lone perpetrator, a German", Herbert Reul, interior minister of North Rhine-Westphalia, home to Muenster, told reporters.
He did not elaborate on how many Dutch were injured or how serious the injuries were.
"This was a disgusting and sad day for the people of Muenster, all of Germany ... and also the people of The Netherlands, who were sitting here and became victims", he said.
As well as the dead, police said 20 were injured - six of them seriously - amid the broken and upturned tables and chairs seen strewn across the pavement in images of the scene.
Police in Germany say there are "no clues" pointing to a possible motive for Saturday's van attack in Muenster.
A witness told German newspaper Bild: "I heard a loud, thumping blow, and suddenly people were yelling "Oh my God".
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According to the German authorities, this incident can not be considered a terrorist attack.
"As of now, we don't have any leads regarding a possible background for the deed", prosecutor Martin Botzenhardt wrote in a joint statement with police. The law enforcement agencies added: "The investigations are being conducted at full speed and in all directions".
Police also dispatched a bomb squad to the scene to check whether there were explosives in the van, the senior security official said. "Everything possible is being done to investigate the act and support the victims and their families".
It was reported by local media that the perpetrator suffered from psychological problems.
A search of the man's Muenster apartment late Saturday turned up more fireworks and a deactivated AK47 assault rifle.
Die Welt said in its online edition the police had detained four men, one of whom they suspected of planning knife attacks at the half-marathon.
Muenster is a popular tourist destination with 300,000 inhabitants, known for its medieval old town, which was rebuilt after the massive destruction during World War II.
The 48-year-old had driven his van into a crowd Saturday afternoon in the historical city center of Muenster.