A big operation is under way. Police are telling people to stay at home and avoid the streets, the BBC said.
Several people have also been injured at the shopping centre in the north-western Moosach district.
Reports speak of one or more attackers. Some shopworkers are reportedly unable to leave the building.
Read alsoTerrorist attack in Nice: Many dead as lorry hits crowdThere is no information about a possible motive for the attack.
The security forces have been on alert after a teenage migrant stabbed and injured five people on a train in Bavaria on Monday.
The authorities had warned of the danger of further attacks.