CNN said three people are dead.
A big operation is underway in Munich. Police have told people to stay at home and avoid the streets.
Several people have also been injured at the shopping centre in the north-western Moosach district.
According to reports, there is one attacker.
Some shopworkers are reportedly unable to leave the building.
The security forces have been on alert after an Afghan teen attacked and severely injured five people with an axe on a train in Bavaria on Monday.
The authorities had warned of the danger of further attacks.
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