"There are strong indications at the moment that this was a lone perpetrator and that there were no links to the terror scene," federal Interior Minister Horst Seehofer told reporters at the site of Saturday's attack, where local people laid flowers in memory of the victims.
The 48-year-old German driver identified as Jens R. shot himself dead immediately after the rampage.
Far-right opponents of Chancellor Angela Merkel's refugee policy had suggested in the immediate aftermath of the attack it might be an Islamist act of terror, while some media reported the killer had links to right-wing extremist organisations.
But authorities said there was a record of incidents related to the perpetrator's impaired mental health since 2015, and that he had talked of suicide in an email to acquaintances in late March.
Police and prosecutors said he had faced allegations of threats, property damage and fraud in 2015 and 2016, all of which were dropped.
And broadcaster NTV reported he had threatened family members with an axe in 2014 and 2015.
Forensics scour the scene in Muenster on Saturday night. Source: EPA
In the van, police found the gun used by the driver to kill himself, a blank-firing pistol along with some powerful fireworks.
A search of the man's Muenster apartment turned up more fireworks, a deactivated AK47 assault rifle and canisters of gas and other fuel.
The driver, reportedly a wealthy industrial designer, had two other flats in the eastern cities of Dresden and Pirna which were also being searched.
The daily Sueddeutsche Zeitung said police had found an 18-page missive in his Pirna home in which he wrote of his anguish due to serious problems with his parents, "repeated nervous breakdowns" and "explosions of aggression" as well as a botched medical operation.
'No Islamist connection'
Armed police cordoned off a wide area around the scene of the attack Saturday, urging residents to avoid the city centre to allow investigators to get to work amid initial fears the country had suffered an extremist assault.
"It's still unbelievable for me, but these days anything can happen," said Hubert Reckermann, a local man in his late 60s on Sunday.
"You can't really defend yourself against people with psychiatric problems."
The two victims killed in Muenster were a 51-year-old woman and a 65-year-old man, both from northern Germany.
As well as the dead, police said 20 were hurt -- some with life-threatening injuries.
The foreign ministry in the Netherlands said two of the injured were Dutch, one of whom was in a critical condition.
Germany has been on especially high alert for jihadist attacks after several claimed by the Islamic State group.
But "we know with high probability that it was a lone perpetrator, it was a German, not a refugee," said North Rhine-Westphalia state interior minister Herbert Reul.
"We know with high probability that there was no Islamist background" to the Saturday afternoon attack, inflicted as locals and tourists enjoyed a sunny spring day, he added.
'Deeply shaken'
Merkel said she was "deeply shaken" by the incident and pledged that "everything possible will be done to determine what was behind this act and to help the victims".
The presidents of Russia and France, Vladimir Putin and Emmanuel Macron, as well as Spanish Prime Minister Mariano Rajoy sent their condolences.
The attack is the latest in a string across Europe in which vehicles have been used to ram into crowds of people in public places.
In a Berlin assault in December 2016, 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 a Christmas market.
He was shot dead by Italian police in Milan four days later while on the run.
In France, the Islamic State claimed a 2016 truck attack in Nice on its July 14 national holiday that killed 86.
And in Spain, the jihadists also claimed a rampage along Barcelona's Las Ramblas boulevard in August 2017 that killed 14 and left more than 100 injured.
