Authorities urged residents to remain inside and put the Bavarian capital on lockdown.
"At the moment no culprit has been arrested," police in the Bavarian capital said on social media as Germany's elite GSG9 anti-terror unit and federal police were called in to help in the manhunt. "The search is taking place at high speed."
Witnesses reported seeing three men with firearms near the Olympia Einkaufszentrum mall.
The city sent a smartphone alert declaring an "emergency situation" and telling people to stay indoors and German rail company Deutsche Bahn stopped train traffic to Munich's main station.
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The attack started at a fast food restaurant shortly before 6 pm local time, police said.
Video obtained by The Associated Press from German news agency NonstopNews showed two bodies with sheets draped over them not far from a McDonald's across from the mall. Another video posted online shows a gunman emerging from the door of the McDonald's, raising what appears to be a pistol with both hands, and aiming at people on the sidewalk, firing as they flee in terror.
He told German broadcaster n-tv that he heard the attacker yell an anti-foreigner slur and "there was a really loud scream."
He said he saw only one attacker, who was wearing jack boots and a backpack.
"I looked in his direction and he shot two people on the stairs," Zequiri said. He said he hid in a shop, then ran outside when the coast was clear and saw bodies of the dead and wounded on the ground.
Germany's Interior Ministry said Munich police had set up a hotline for concerned citizens. Residents of Munich opened their doors to people seeking shelter using the Twitter hashtag #opendoor.
German Chancellor Angela Merkel's was being regularly briefed on the attack, said her chief of staff, Peter Altmaier.