Munich police called on people in the Rosenheimer Platz area, located close to the German city’s downtown, to stay inside after the incident on Saturday morning.
The perpetrator fled the scene.
Police said the motive for the attack was not immediately clear.
None of the injuries were considered life-threatening.
German police special forces have detained a suspect in the knife attack in the southern city of Munich, Bild newspaper said on it website.
The daily did not give a source for its report. Police are expected to hold a news conference in the Bavarian capital around 1000 GMT.