There are reports of at least six people killed, but police have not confirmed that figure.
A big security operation is under way at the Olympia shopping centre in the north-western Moosach district.
Shop workers have been unable to leave the building. There is no information about a possible motive for the attack.
The police Facebook page quoted eyewitnesses as saying they had seen three attackers carrying guns.
Police are now describing it as “an acute terror situation”.
Public transport has been suspended as the extensive security operation continues.
The city’s central railway station has been evacuated.
People stranded by the emergency and unable to get home are being offered shelter by locals. The initiative was launched with the Twitter hashtag #Offentür (open door).
Police helicopters are flying over the city and special forces are involved in the massive police deployment.
The security forces have been on alert after a teenage migrant stabbed and injured five people on a train in Bavaria on Monday in an attack claimed by so-called Islamic State.
The authorities had warned of the danger of further incidents.
A man working at a petrol station in Munich told the BBC: “We see just ambulances and it’s like firemen and police but all this area is evacuated, all the streets.
“Now [there] are no cars just on the side of the streets. All of the streets are blocked. I see that the people are scared. Everybody are running around.”
Munich police said they did not know where “the perpetrators” were. “Look after yourselves and avoid public places”.