The mall near the southern German city's Olympic stadium was surrounded by police after shots were fired.
"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 passers-by looked on.
The shooting comes just days after a teenage asylum seeker went on the rampage with an axe and a knife on a regional train in Germany, injuring five people.
It also follows a truck attack in the French Riviera city of Nice after Bastille Day fireworks last week that left 84 people dead.