The man attacked passersby in five places near Rosenheimer Platz in the eastern part of the city centre at around 0630 GMT, inflicting "light" injuries on four people, a police spokesman told AFP.
The perpetrator of the attack "is still on the run", the local police said on their Twitter account, where they also called on residents to stay inside.
It added "no life threatening injuries" were suffered by the victims.
"We are searching for the perpetrator of the attack with all available police" Munich police said on their Twitter account, adding that for the moment the possible motives for the attack remained unknown.
In July 2016, a German-Iranian teenager who police say was obsessed with mass murderers, shot dead nine people at a Munich shopping mall before turning the gun on himself.