The shooting spree began before 1600 GMT 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.
Three gunmen were involved in the shooting, according to a police statement, citing witnesses.
There was no information about the possible motives of the attack.
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.