Police in the locked-down southern Germany city warned of an "acute terror" situation.
Here is what we know:
What happened?
The shooters armed with "long guns" opened fire at a McDonald's restaurant and continued onto a street before entering the Olympia (OEZ) mall near the Olympic stadium in Munich.
The shooting started shortly before 1600 GMT and authorities said witnesses reported seeing three gunmen.
A video posted on social media appeared to show a man dressed in black walking away from the McDonald's while firing repeatedly on people as they fled.
Authorities evacuated the main train station in the city of some 1.4 million, while metro and bus transport services were suspended in the wake of the assault.
The shopping centre, which opened in the 1970s and bills itself as Bavaria's biggest, was surrounded by armed police, while a helicopter buzzed overhead.
The Olympia mall is near the stadium for the 1972 Olympics and the athletes' village, which was the site of the massacre of 11 Israeli athletes by the Palestinian Black September group.
Munich police said on Twitter that there were an "unknown number of injured people".
Was it a terror attack?
A Munich police spokesman told AFP they suspected "terrorism" in the rampage, while German news agency DPA quoted police as warning of an "acute terror situation".
The three attackers were still at large, fleeing in the direction of a nearby metro station, media reports said.
There was no information about the possible motives of the shooting, but Europe has been on alert in the wake of a string of attacks including bombings in neighbouring France and Belgium.
The shooting spree comes on the fifth anniversary of right-wing fanatic Anders Behring Breivik's massacre in Norway that killed 77 people.
Train attacks
The violence comes just days after a teenage asylum seeker went on a rampage with an axe and a knife on a regional train in Germany on Monday, injuring five people, two of them critically.
Interior Minister Thomas de Maiziere said the teenager was believed to be a "lone wolf" attacker who appeared to have been "inspired" by the Islamic State group but was not a member of the jihadist network.
The assailant had arrived as an unaccompanied minor in Germany in June 2015 and had been staying with a foster family in the region of the attack for the last two weeks.
In May, a mentally unstable 27-year-old man carried out a knife attack on a regional train just southeast of Munich, killing one person and injuring three others.
Migrant influx
Bavaria became the main gateway for hundreds of thousands of migrants and asylum seekers arriving in Germany.
Hate crimes and attacks against migrants exploded after arrivals spiked to more than one million last year, mostly from the Middle East and Africa.
Some 923 offences against refugee shelters were reported in 2015, compared to 175 the previous year, according to figures from the Interior Ministry.
Of these, 177 were acts of violence, up from 26 in 2014.
