It also occurred on the one-year anniversary of the Stockholm terror attack in Sweden where a suspect drove a stolen truck into a crowd of pedestrians on a busy street, and four people were killed with several other people injured.
"The scenario is such that an attack can not be ruled out", a security source was quoted by news agency Reuters.
On Twitter, police told people to avoid the area near the Kleiner Kiepenkerl restaurant, saying there had been deaths and injuries. The tragedy was labeled as a terrorist attack by law enforcement officials shortly thereafter.
Images on social media showed smashed and upturned tables and chairs strewn across the pavement outside an eaterie in the centre of the picturesque medieval city. The Sueddeutsche Zeitung newspaper reported the dead suspect was a German national with a history of psychological trouble and that police were already searching his home for clues.
The mayor of Muenster says authorities don't yet know the motive behind the van crash.
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The man was part of a team of the Air Force's six best F-16 pilots, who do flight demonstrations and air shows across the country. Air Force's elite Thunderbirds team was killed in a fighter jet crash Wednesday in central Nevada, military officials said.
Shocking pictures emerged from the scene of the crash showing a panicked and chaotic scene, as people rushed to the aid of the injured.
While Markus Lewe, Münster's mayor, said, 'The whole of Münster is in mourning after this bad event. It happened in a pedestrian area of the historic city as many people were out enjoying the warm spring sunshine on Saturday afternoon.
"At the moment, there is no evidence that there is any Islamist background" to the attack, said Herbert Reul, the interior minister of North-Rhine Westphalia, the state where Münster is located.
"I'm deeply shocked by the very bad events in Muenster", Merkel said in a statement.
Ulrike Demmer, the federal government's deputy spokesperson, said the government's thoughts were with the victims and their families. In December 2016, a Tunisian man whose asylum request had been rejected crashed a truck through a crowded Christmas market in Berlin, killing 12 and injuring 56.