Police arrested the perpetrator after he was overpowered at the station in Grafing, 25 miles south-east of central Munich.
One of the victims died of his injuries, Bavarian Radio and other local media reported.
Ebersberger newspaper said the attacker was a German citizen who is not known to the police.
The Bavarian prosecutors office has started criminal investigation and has imposed a news blackout. The station has been cordoned off by police.
Germany, which is playing a supporting role in the fight against Islamic State, has not suffered the kind of major attack by Islamist militants experienced by neighbouring France and Belgium.
Attacker`with apparent Islamist motive` kills one at train station near Munich
10 May 2016
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One person has died and three others are injured after a man launched a knife attack at a train station in southern Germany.
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