The incident took place at Grafing S-Bahnhof in the suburban Ebersberg area of the city.
Police spokeswoman Michaela Grob said the man was arrested and authorities were working to identify him. He has no criminal record. The offender is reportedly a German citizen.
German police are now questioning eyewitnesses for further examination.
Four men are being treated for life threatening injuries following the attack at 5am (3am GMT) according to local radio reports.
A spokesperson at the Bavarian state criminal investigation office told The Independent one of the victims was initially in a critical condition but died later in hospital.
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