Authorities believe the 27 year-old attacker had psychological and drug problems.
The attack occurred on a sunny morning in the quiet Bavarian town of Grafing, about 40 kilometres east of Munich.
German police say the man assaulted several people at the local railway station, before chasing and stabbing another two men riding by on their bikes.
One man later died from his wounds.
Some witnesses have reported the attacker was shouting Allahu Akbar - God is Great in Arabic - and muttering, "you non-believers have to die."
But speaking in Munich, Vice-President of the State Criminal Investigation, Petra Sandles says the man is a German national and appeared to be acting alone.
"So far we have no indications in our investigation of more suspects, we also have no indications of him being part of an Islamist network. We couldn't find out what connection he had with Grafing. So far it seems to be a crime scene chosen by coincidence."
It appears the man, from the town of Giessen, had been suffering from mental illness.
Head of the Criminal Division, Lothar Koehler, says the man had been seen in recent days suspected of being on drugs and displaying behaviour indicating he was psychologically disturbed.
"Two days ago an incident occured, where police attention was pointed to the 27 year-old for uttering confused things. The police were called, but couldn't determine any indications of him being a threat to himself or others. A medical consultation was recommended, which the suspect then underwent."
The incident has unnerved passengers on a train line popular with Bavarians commuting to the capital Munich.
"Yeah it seems very unusual, this is the second time I've been here, I've never heard of anything like this happening in a small town like this. It's such a beautiful place, it's hard to believe something like that would happen here."
"I always felt very safe, so there's a bit to reflect on about whether you can really feel safe, that's now probably changed. I also have to first process that."
A 56 year-old man died in hospital after being stabbed with the attacker's 10 centimetre-bladed knife.
Three others were seriously wounded.
Security forces are on high alert in the country with hundreds of German-born people who joined jihadist groups in Syria and Iraq now returning home.
But it seems police view this incident as more the work of one man's disturbed mind than an international terror network.
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