The attack appears to have begun inside a train while it was standing at the station.
The first victim was a 50-year-old passenger on the train, who has since died of his wounds in hospital.
The attacker then ran out of the train onto the platform.
“I’ll stab you all,” he shouted, according to eyewitnesses, as well as “You infidels!” and “Allahu akbar!”
One witness told Sueddeutchse Zeitung newspaper the train driver intervened at one point, and tried to beat the man off with a fire extinguisher.
Prosecutors say they have “no concrete information” that the man had any connections to Islamic extremists, and there is no evidence of any link to Islamic State of Iraq and the Levant (Isil).