The Bild newspaper reported that a gunman ran through the mall near the Olympic stadium in the southern German city, firing on several people before fleeing in the direction of a nearby metro station.
"There are several dead and injured," a Munich police spokeswoman told AFP, adding that the shooting had started shortly before 1600 GMT at a McDonald's restaurant.
"The attacker, or several attackers , are apparently still at large."
Europe has been on alert for terrorism in the wake of a string of attacks including bombings in neighbouring France and Belgium.
The OEZ shopping centre was surrounded by armed police who were hunting for the attacker, while a helicopter flew overhead.
"There is a major police operation under way in the shopping centre,"
Munich police said on Twitter, urging people to avoid the area.
Emergency vehicles were seen in the streets outside, as shoppers rushed away from the mall, some carrying children in their arms.
"Attention -- avoid the neighbourhood around the OEZ. Stay in your homes. Leave the street," the Munich police tweet said.
Germany has so far escaped the kind of large-scale jihadist attacks seen in neighbouring France.