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).
One of the injured is still in critical condition, according to the Bavarian authorities.
This is Germany’s third knife attack with an apparent Islamist motivation since September.
In February a 15-year-old girl identified as Safia S. stabbed a policeman in the neck with a kitchen knife in what prosecutors later said was an Isil-inspired attack.
She attacked the officer during a routine check at Hanover train station in the country’s north before being overpowered by another police officer.
Federal prosecutors later said the teenager had “embraced the radical jihadist ideology of the foreign terrorist group Islamic State of Iraq and Syria” and was in contact with an Isil fighter in Syria.
Last September a 41-year-old Iraqi man identified as Rafik Y. stabbed and seriously wounded a policewoman in Berlin before another officer shot him dead.
The man had previously spent time in jail for membership of a banned Islamist group and had been convicted in 2008 of planning an attack in Berlin against former Iraqi prime minister Iyad Allawi.
Elsewhere in Europe today, Italian police have arrested two Afghan men on suspicion of planning to carry out terrorist attacks in Britain and Italy, including targets in London and the Colosseum in Rome.
The two men, named as Hakim Nasiri, 23, and Gulistan Ahmadzai, 29, were arrested in the southern city of Bari, on the Adriatic coast, writes Nick Squires in Rome.
Nasiri was arrested on terrorism charges while Ahmadzai was detained on charges of aiding illegal immigration.
Police are searching for three other suspects involved in the same alleged plot.
Meanwhile, Justin Huggler in Berlin writes:
Police in neighbouring Czechia (Chezch Republic) have evacuated several schools, town halls and railway stations across the country after receiving an anonymous tip-off that they were to be targetted in coordinated bomb attacks.
The main train station and municipal buildings in the capital Prague were affected, along with the train station and city hall in the western city of Pilsen.
A total of 14 different locations around the country were involved. The evacuations began at around 10am local time (am BST) after the authorities received detailed tip-offs including the timings bombs would go off at the various locations.
In the central city of Pardubice, which was also affected, staff at the city hall said they had received a tip-off in a phone call.
“At about 8.30am we received an anonymous phone call saying that a bomb would go off in the city hall at 12pm. We immediately contacted the police,” Radim Jelinek, a spokesman for the municpality said.
The anonynpus tipster apaprently made no attempt to hide their telephone number.
“We handed over the phone number of the anonymous caller, because it showed up in the caller ID, “Mr Jelinek said.