The shooter killed nine people then himself, and also injured at least 16 more.
Police currently believe that an 18-year-old German-Iranian acted alone, killing nine people and then himself on Friday.
They have not yet identified a motive; the man had no criminal record. Munich spent hours under lockdown.
Police said it was too early to comment on a possible motive, but added they believed the shooter to be a young German-Iranian resident of Munich, who had lived there “for a long time.” He had no criminal record.
The shooter opened fire near a fast-food restaurant and then again at the nearby Olympia shopping centre in the north of the Bavarian capital, just before 6 p.m. local time.
He subsequently fled the scene, prompting a city-wide manhunt and state of emergency.
Police at one point engaged and shot at him, only for him to escape. They later found him dead, killed by a self-inflicted gunshot. The corpse was roughly one kilometre (just over half-a-mile) from the scene of the initial shooting.
The city was in lockdown for hours; 2,300 emergency services personnel were mobilised, public transport was suspended until the early hours of Saturday, the main train station evacuated.
In a late-night press conference, shortly after police cautiously announced the all-clear, Munich Police boss Hubertus Andra described the operation as “without doubt my most difficult day” in the role.
“Three youngsters” were among the dead, Andra said, while children were also among the injured.
“The motive, and the background of the crime are still totally unclear, the investigators are working full tilt and will continue into the night,” added Andra said, stating that the process should move relatively quickly, as police were confident that they had identified the suspect.