The shooting spree began before 2130 IST at a McDonald's restaurant and continued on a nearby street before the gunmen moved into the mall near the Olympic stadium in the southern German city, a police spokeswoman said.
"There are several dead and injured," the spokeswoman said, without confirming the death toll of six.
Munich's main train station has been evacuated and metro and bus transport in the city suspended, officials said.
There was no information about the possible motives of the attack.
More From This Section
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, while a helicopter buzzed 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.
Germany has so far escaped the kind of large-scale jihadist attacks seen in France.
But the shooting comes just days after a teenage asylum seeker went on a rampage with an axe and a knife on a regional train in Germany on Monday, injuring five people, two of them critically.
One victim is still fighting for his life, the hospital treating him said today.
Interior Minister Thomas de Maiziere said the teenager was believed to be a "lone wolf" attacker who appeared to have been "inspired" by the Islamic State group but was not a member of the jihadist network.
The attacker is believed to be either Afghan or Pakistani and investigators are still trying to determine his identity.
The train rampage triggered calls by politicians in Bavaria, of which Munich is the capital, to impose an upper limit on the number of refugees coming into the country.
The assailant had arrived as an unaccompanied minor in Germany in June 2015 and had been staying with a foster family in the region of the attack for the last two weeks.