Multiple shots were fired on Hanauer Street before the attack moved to the Olympia Einkaufszentrum shopping centre in the south German city at around 6pm on Friday.
Witnesses told police there were three gunmen, who are now on the run.
Munich Police tweeted: “The suspects are still on the run. Please avoid public places.”
The force added: “Please don’t take Fotos or Video of Police Action in order to avoid any helpful Information for the suspects.”
Munich’s public transport system has been shut down, nightclubs closed and drivers urged to clear motorways as the manhunt continued.
Foreign Secretary Boris Johnson said on Twitter: “Deeply shocked & saddened by #Munich shootings. My thoughts are w/ the victims, their loved ones & all #Germany at this time.”
Jeremy Corbyn tweeted: “Shocking news from Munich - my thoughts are with the people of the city at this time.”
In unverified footage, a man with dark hair, wearing a black T-shirt and denim trousers, appears to take aim at people outside a McDonald’s restaurant near the Olympia-Einkaufszentrum metro station.
He raises his arms, apparently holding a shotgun, and appears to fire at people outside the restaurant, who can be seen running for cover.
The sound of multiple shots being fired can be heard as shoppers and passers-by run for cover.
People were seen fleeing from the building in another video posted on social media.
In a picture posted online, a person can be seen lying on the ground covered in blood.
Police have responded to the attack in large numbers. Dozens of vehicles can be seen lining the street outside the shopping centre, and a number of armed officers and a helicopter are at the scene.
A cordon appears to be in place and the area has been evacuated.
The shopping centre in the northern part of Munich is not far from the city’s Olympic stadium in the Moosach district of the Bavarian capital.
The number of casualties or any fatalities have not yet been confirmed by authorities.
British nationals in Germany are being advised to comply with instructions from local authorities.
A Foreign Office spokesman said: “We are urgently investigating an incident in Munich and stand ready to provide assistance to British nationals.”
There are unconfirmed reports of shootings in other parts of the city, Munich Police said.
It tweeted: “Unconfirmed reports of more violence and possible #gunfire in the City Center. Situation is unclear. Please avoid public Areas.”
Munich Police said in a statement: “At around ten to six today there were witnesses who called the police and said there was a shooting at the Hanauer Street.
“The shooting moved from that street to the shopping centre. The witnesses said there were three different people with weapons.”
The police said that they did not have any details about the number of victims or injuries and that no arrests had been made.
They said that the Metro system is not working at the moment and urged people to stay at home or seek shelter inside nearby buildings.