Police are investigating whether one of the bodies is that of a perpetrator. At least 10 people have been wounded.
Three armed attackers were earlier reported to be on the run. Police urged people to avoid public places.
The attack was at the Olympia mall in the north-western Moosach district. Public transport has been suspended.
Police helicopters are flying over the city and the elite border security unit, GSG9, has been flown in.
The body of the suspected attacker was found about 1km (0.6 miles) from the shopping centre, local media reported, and police were using a robot to check it for explosives.