Authorities told the public to get off the streets as the city - Germany's third biggest - went into lockdown with transport halted and highways sealed off.
The shooting spree began before 1600 GMT at a McDonald's restaurant and continued on a nearby street before the gunmen moved into the mall near the Olympic stadium in the southern German city, a police spokesperson said.
đWATCH terrorrist shooting in #Munich, #Germany https://t.co/XqOGYpLntq
— (((Sushant))) (@spati2012) July 22, 2016
The city was placed under a state of emergency as police hunted for them.
"We are telling the people of Munich there are shooters on the run who are dangerous," he said. "We are urging people to stay indoors."
AÂ ninth body had also been found and they were checking to see it was one of the gunmen, police added.
We are verifying the possibility of one dead person being involved in the shooting, #MĂŒnchen, #oez, #SchieĂerei
— Polizei MĂŒnchen (@PolizeiMuenchen) July 22, 2016
There was no information about the possible motives of the attack.
Europe has been on alert for terrorism in the wake of a string of attacks including bombings in neighbouring France and Belgium.
The OEZ shopping centre was surrounded by armed police, while a helicopter buzzed overhead.
https://twitter.com/ReutersLive/status/756587153577152512
"Many shots were fired, I can't say how many but it's been a lot," said a shop worker hiding in a store room inside the mall.
"There is a major police operation under way in the shopping centre," Munich police said on Twitter, urging people to avoid the area.
Meiden Sie öffentliche PlĂ€tze in #MĂŒnchen. Die Lage ist noch unĂŒbersichtlich. #oez #SchieĂerei
— Polizei MĂŒnchen (@PolizeiMuenchen) July 22, 2016
"Attention - avoid the neighbourhood around the OEZ. Stay in your homes. Leave the street," the Munich police tweet said.
Germany has so far escaped the kind of large-scale extremist attacks seen in France.
But the shooting 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.
One victim is still fighting for his life, the hospital treating him said Friday.
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 extremist network.
Authorities said he shouted "Allahu akbar" (God is greatest) three times as he ran through the carriage slashing passengers on the train near the southern city of Wuerzburg.
The attacker is believed to be either Afghan or Pakistani and investigators are still trying to determine his identity.
The train rampage triggered calls by politicians in Bavaria, of which Munich is the capital, to impose an upper limit on the number of refugees coming into the country.
Germany plans to assume greater security role
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.
A record 1.1 million migrants and refugees were let in to Germany last year, with Syrians making up the largest group followed by Afghans.
In the latest attack in France, 31-year-old Mohamed Lahouaiej Bouhlel used a truck to mow down 84 people, including children, in the Riviera city of Nice last week.
It was the third major attack on French soil in the past 18 months, after the carnage in Paris in November and the shootings at satirical magazine Charlie Hebdo and a kosher supermarket in January 2015.
Islamic State claims first German attack with train axe assault
In March, Islamic State-claimed suicide bomb attacks at Brussels airport and a city metro station left 32 people dead.
In May in Germany, a mentally unstable 27-year-old man carried out a knife attack on a regional train in the south of the country, killing one person and injuring three others.
Obama vows support for Germany after Munich shooting
US President Barack Obama has pledged support to Germany in the wake of the deadly shooting rampage.
Watch as @POTUS provides an update on the developing situation in #Munich, Germany: https://t.co/RKJMCirtS9
— White House Archived (@ObamaWhiteHouse) July 22, 2016
Obama, speaking at a meeting with law enforcement officials, said he had been briefed on the unfolding drama in Germany, where at least six people are believed dead in a shooting at a shopping center in Munich.
"Our hearts go out to those who may have been injured. It's still an active situation, and Germany's one of our closest allies, so we are going to pledge all the support that they may need in dealing with these circumstances," he said.
At the State Department, spokesperson Elizabeth Trudeau said US officials were working with local authorities to determine if any US citizens were affected by the incident.
German magazine cites sources saying shooter killed himself
German magazine Focus cited police sources as saying one of the gunmen on the rampage in Munich had shot himself in the head and died.
Merkel to convene German security council
German Chancellor Angela Merkel will convene her security council Saturday to address the deadly shooting rampage in Munich, her chief of staff Peter Altmaier said.
Altmaier told ZDF public television on Friday that Merkel was being "constantly briefed" on developments in the southern city, where police say up to three gunmen are still at large.
"The cabinet ministers concerned are on their way to Berlin," he added.
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