"At the moment no culprit has been arrested," police in the Bavarian capital said on social media. "The search is taking place at high speed."
The city of Munich sent a smartphone alert telling people to stay indoors and German rail company Deutsche Bahn stopped train traffic to Munich's main station.
Police said witnesses reported seeing three people with firearms near the Olympia Einkaufszentrum mall.
Munich police spokeswoman Claudia Kuenzel told The Associated Press there were "several dead and wounded" in the shooting. She could not provide exact numbers. Bavarian public broadcaster Bayrischer Rundfunk and Munich-based Focus magazine, citing sources they did not identify, said six people were killed.
Munich police spokesman Thomas Baumann told German news agency dpa the attack started at a fast food restaurant shortly before 6 p.m. local time.
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.
Bayrischer Rundfunk reported that shops in the center of Munich had closed with customers inside though police said reports of shots fired at a location downtown had been a false alarm.
Police responded in large numbers to the mall in the northern part of Munich, not far from the city's Olympic Stadium in the Moosach district of the Bavarian capital.
It was also not far from where Palestinian attackers opened fire in the Olympic Village in 1972, killing 11 Israeli athletes.
It was the second attack in Germany in less than a week. On Monday, a 17-year-old Afghan wounded four people in an ax-and-knife attack on a regional train near the Bavarian city of Wuerzburg, and another woman outside as he fled. All survived, although one man from the train remains in life-threatening condition. The attacker was shot and killed by police.
The Islamic State group claimed responsibility for the train attack, but authorities have said the teen likely acted alone.
Jordans reported from Berlin. Associated Press staffers David Rising and Ferdinand Ostrop contributed from Berlin.