The incident took place on Kapuzinerplatz at around 2.15 pm, and the entire area was then blocked off, Focus reports.
The man, who is reportedly 29 and from Italy, was brought to hospital with a leg injury.
The police had earlier received reports that a man "who appeared confused" was threatening bystanders with a weapon.
When police arrived at the scene, they ascertained that the man was carrying a pair of scissors. When they tried to calm him he became more aggressive.
According to Focus, the man then stabbed at a police car and an officer responded by firing a warning shot in the air. When he then attacked one of the officers, they shot him twice, once in the leg, once in the torso area.
The man's condition is said to be stable.
Munich was shocked recently when a young man attacked commuters at a quiet train station in the early hours of the morning on May 10th.
One of his victims died of his wounds while three were seriously injured. The attacker was later put into psychological care.