The third attack on civilians in Europe in just over a week sent panicked shoppers fleeing the mall in Germany's third largest city as elite police launched a massive operation to track down what had initially been thought to be up to three assailants.
German Chancellor Angela Merkel will convene her security council on Saturday after the shooting, which came just days after an axe rampage on a train in the same German state of Bavaria and just over a week after a truck attack in the French Riviera city of Nice that killed 84 people.
"The perpetrator was an 18-year-old German-Iranian from Munich," police chief Hubertus Andrae told reporters, adding that he had no criminal record.
"The motive or explanation for this crime is completely unclear," he said.
Earlier, a police spokesman had said terrorism was suspected, without revealing any immediate indications of an Islamist link.
Armed with a handgun, the attacker opened fire at a McDonald's restaurant early Friday evening and continued in the street before entering the mall, killing nine people and wounding 16, according to the latest toll.
Andrae said there were young people among the dead and that some of the injured were children.
A police patrol had shot and wounded the gunman but he managed to escape, he said.
The suspected attacker's body was later found about one kilometre (half a mile) from the mall, German DPA news agency reported.
"We found a man who killed himself. We assume that he was the only shooter," police said on Twitter.
'Terror and inhuman violence'
A video posted on social media appeared to show a man dressed in black walking away from a McDonald's while firing repeatedly on people as they fled screaming.
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.
Survivors described terrifying scenes.
"We entered McDonald's to eat... then there was panic, and people ran out," one woman told Bavarian public television. She said she heard three gunshots, "children were crying, people rushed to the exit in panic".
Police initially believed there could be up to three assailants.
But Andrae later clarified that two others who had been thought to be linked had "absolutely nothing to do" with the attack -- and that they were simply fleeing the scene.
Munich's main train station was evacuated and metro and bus transport in the city suspended for several hours while residents were ordered to stay inside, leaving the streets largely deserted.
By early Saturday, transport services were running again.
"We are determined to do everything we can so that terror and inhuman violence stand no chance in Germany," Merkel's chief of staff Peter Altmaier said.
German President Joachim Gauck said he was horrified by the "murderous attack" at the mall, while US President Barack Obama and French counterpart Francois Hollande voiced staunch support for their close ally.
"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," Obama said.
Austria said it had "significantly" tightened security measures in states sharing a border with Germany and put its elite Cobra police force on high alert.
The attack came just days after a teenage asylum seeker went on a rampage with an axe and a knife on a train on Monday near Wuerzburg, also in Bavaria, injuring five people.
Interior Minister Thomas de Maiziere had said the attacker was believed to be a "lone wolf" who appeared to have been "inspired" by Islamic State group but was not a member of the jihadist network.
That rampage triggered calls by politicians in Bavaria to impose an upper limit on the number of refugees coming into Germany, which accepted a record 1.1 million migrants and refugees last year.
Munich Olympic massacre
The Munich mall is near the stadium for the 1972 Olympics and the athletes' village which was the site of the hostage-taking and massacre of Israeli athletes by the Palestinian Black September group during the Games.
The shooting coincided with the fifth anniversary of the massacre of 77 people in Norway by rightwing fanatic Anders Behring Breivik.
Europe has been on alert for terrorism in the wake of a string of attacks in neighbouring France and Belgium claimed by the IS.
The mall shooting occurred just eight days after 31-year-old Mohamed Lahouaiej Bouhlel used a truck to mow down 84 people, including children, after a Bastille Day fireworks display in Nice, the third major attack on French soil in the past 18 months.
In March, IS claimed suicide bombings at Brussels airport and a city metro station that left 32 people dead.
In May, a mentally unstable 27-year-old man carried out a knife attack on a regional train in Bavaria, killing one person and injuring three others.