The suspect is a 20-year-old Syrian man, while three of the four wounded -- ages 15, 24 and 51 -- are also Syrian nationals, police said in a statement Thursday.
An earlier statement said the suspect was arrested at the scene following the incident on a train carrying around 500 passengers as it passed near the village of Strasskirchen.
"At around 1:55 pm today a man on an ICE train travelling towards Vienna injured several people with dangerous objects," police said.
In an update, police said the suspect had been "subdued by other passengers" before being detained by law enforcement.
The suspect "apparently had a hammer and an axe" at the time of the attack, but investigators were not yet sure "to what extent the two objects were used simultaneously or independently", police spokesman Guenther Tomaschko told AFP.
The motive and circumstance around the attack remain unclear, Tomaschko said, adding he didn't want to "speculate" about links between those with Syrian nationality.
The nationality of the fourth victim, age 38, was not specified.
According to Bavarian interior minister Joachim Herrmann, the suspect "arrived in Austria as a refugee" and "was legally travelling" after obtaining a residence permit in that country.
Austrian authorities are also investigating the suspect's history and whereabouts in the Vienna region where he likely resided, Herrmann said.
Among the victims was a Syrian woman and her son, he added.
Police would not specify the severity of the victims' injuries, although an earlier statement said four people received "minor injuries".
Rail operator Deutsche Bahn said it was "appalled" by the "violent attack" on the train, which had been travelling from Hamburg.
"Our thoughts and sympathy are with the injured and all those who are now coming to terms with what they have experienced," a spokesman said.
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