A suspect was arrested a few hours later, and authorities were working to determine whether he was the assailant.
Police received initial reports of an attack in the Haidhausen area, just east of downtown Munich, at about 8:30 a.m., spokesman Marcus da Gloria Martins said.
They determined that a lone attacker apparently had gone after passers-by indiscriminately with a knife.
The assailant attacked six people - five men and one woman - at different sites in the area, with four of them wounded and none seriously, da Gloria Martins said.
After the attack, police took to Twitter to warn people in the Rosenheimer Platz area to stay indoors and cautioned them to avoid the area around the nearby Ostbahnhof railway station and a park amid conflicting accounts of the direction in which the suspect fled.
Police also issued a description of the suspect, who they said appeared to be about 40 years old and had a black bicycle, gray trousers, a green jacket and a backpack. They described him as having a "corpulent figure" and added that he had short blond hair and was unshaven.
"We can't yet confirm whether he is the perpetrator," da Gloria Martins said.
There was no immediate word on a possible motive.
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