Images on social media showed smashed and upturned tables and chairs strewn across the pavement in the centre of the picturesque medieval city.
At least 20 people were injured, six of them seriously, according to police, while media reports said the driver had been behind the wheel of a delivery van.
A police spokeswoman in the western city, Vanessa Arlt, told AFP that the driver of the vehicle “shot himself”.
“The perpetrator drove into several cafe and restaurant terraces in a major square in the centre of Muünster,” Arlt added.
German authorities have found no evidence of an Islamist motive behind the deadly vehicle rampage, state interior minister Herbert Reul said.
“The perpetrator who recklessly sped into a crowd of people after 3pm is, according to the current stage of the investigation, a German citizen and not, as has been claimed everywhere, a refugee or something like that,” Reul, of North Rhine-Westphalia state, told reporters.
“There is no indication at the moment that there is any Islamist connection,” he said, after correcting the number of total dead down from four to three including the driver.
Media reports said the driver was a German national in his late 40s with a history of mental health problems. He was described as “psychologically disturbed” and according to public broadcaster ZDF had recently attempted suicide.
At least 20 people were injured in the incident, six of them seriously.
“There was a bang and then screaming. The police arrived and got everyone out of here,” an employee of one the cafes hardest hit by the rampage told rolling news channels N24 and NTV. “There were a lot of people screaming. I'm angry — it's cowardly to do something like this.”
Armed police were deployed and officers urged residents to avoid the city centre to allow investigators to get to work amid initial fears the country had suffered another extremist assault.
Germany has long braced for more violence after several attacks claimed by the Islamic State jihadist group, the bloodiest of which was a truck rampage through a Berlin Christmas market in December 2016 that left 12 people dead.
Images broadcast by German television showed police and firefighting vehicles clustered around a street in the centre of the city of 300,000 people. Armed police were deployed and officers urged residents to avoid the city centre to allow investigators to get to work.
“Terrible news from Münster,” German government spokeswoman Ulrike Demmer said in a tweet. “Our thoughts are with the victims and their loved ones.”
Germany has seen a number of other jihadist attacks in recent years. In the Berlin Christmas market attack, Tunisian asylum seeker Anis Amri, hijacked a truck and murdered its Polish driver before killing another 11 people and wounding dozens more by ploughing the heavy vehicle through the festive market in central Berlin. He was shot dead by Italian police in Milan four days later while on the run.
Germany has since been targeted again in attacks with radical Islamist motives. In July 2017, a 26-year-old Palestinian asylum seeker wielding a knife stormed into a supermarket in the northern port city of Hamburg, killing one person and wounding six others before being detained by passers-by. German prosecutors said the man likely had a “radical Islamist” motive.
And at the end of October, German police arrested a 19-year-old Syrian identified only as Yamen A. suspected of planning a “serious bomb attack” using powerful explosives.
Isis also claimed responsibility for a number of attacks in 2016, including the murder of a teenager in Hamburg, a suicide bombing in the southern city of Ansbach that wounded 15, and an axe attack on a train in Bavaria that left five injured.
Germany an Isis target
Germany remains a target for jihadist groups, in particular because of its involvement in the coalition fighting Isis in Iraq and Syria, and its deployment in Afghanistan since 2001.
German troops in the anti-Isis coalition do not participate in combat operations but support it through reconnaissance, refuelling and training.
Germany's security services estimate there are around 10,000 Islamic radicals in Germany, some 1,600 of whom are suspected of being capable of using violence.
Chancellor Angela Merkel has allowed in more than one million asylum seekers in the past two years — a decision that has driven the rise of the far-right Alternative for Germany (AfD) party, which charges that the influx spells a heightened security risk.
Isis also claimed several similar attacks in Europe, including a rampage along Barcelona's Las Ramblas boulevard in August 2017 that killed 14 and left more than 100 injured.
The deadliest such incident in recent years was in the French resort city of Nice in 2016, where a man rammed a truck into a crowd on France's national July 14 holiday, killing 86 people.