The southern city was in lockdown after the shootings, which saw panicked shoppers fleeing the Olympia mall as anti-terror police launched a massive operation to track down the assailants.
"We suspect terrorism," a police spokesman in the Bavarian capital said, but there were no immediate indications of an Islamist link.
A video posted on social media appeared to show a man dressed in black walking away from a McDonald's restaurant while firing repeatedly on people as they fled screaming.
Germany has so far escaped the kind of large-scale jihadist attacks seen in neighbouring France and the motives and identities of the gunmen were not yet known. Police said up to three shooters were still at large and reported to be armed with "long guns".
Munich's main train station was evacuated and metro and bus transport in the city suspended while residents were ordered to stay in their homes, leaving the streets largely deserted.
Chancellor Angela Merkel will convene her security council today to address the deadly rampage in the European economic powerhouse which took in more than one million migrants and refugees last year.
"We are determined to do everything we can so that terror and inhuman violence stand no chance in Germany," her chief of staff Peter Altmaier said.
It is the third strike against civilian targets in Europe in eight days, following an axe rampage on a train in the same German state of Bavaria on Monday and the truck attack in France on July 14.
One spokesman said the body of a man had been found near the mall and investigators were trying to determine whether he was one of the assailants.
Another video appeared to show a gunman on the roof of a parking garage as he exchanged insults with people on a nearby balcony who referred to him a foreigner.
"I'm German, I was born here," the assailant is heard to reply.
The spree began before 1600 GMT at the McDonald's and continued on a nearby street before the gunmen moved into the Olympia centre--which lies not far from the scene of the 1972 Olympics massacre.
Shoppers rushed away from the mall, some carrying children in their arms, as the building was surrounded by armed police and emergency vehicles, while helicopters buzzed overhead.
Europe has been on alert for terrorism in the wake of a string of attacks in neighbouring France and Belgium claimed by the Islamic State jihadist group.

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