The incident occurred shortly before 01:00 local time at the station in Rosenheim, a major rail hub in Upper Bavaria. The woman was taken to hospital but died from what police described as "severe" injuries.
Officers arrested a 27-year-old German man from the Fürstenfeldbruck district immediately after the attack. He was expected to appear before magistrates later on Sunday, according to German news agency DPA. Police have called for witnesses who may have seen "an argument or physical altercation" at the station late on Saturday or early on Sunday to come forward.
It is not yet clear whether the victim and suspect knew each other, DPA reported. Investigators from the criminal investigation department are working with the public prosecutor's office to establish the circumstances and motive.
The attack comes during the Rosenheimer Herbstfest, a local beer festival similar to Munich's Oktoberfest, which is currently underway in the area. Rosenheim Mayor Abuzar Erdogan said there were "no indications of a security threat in our city or of any link to our Herbstfest," and described the investigation as urgent.
The UK Foreign Office confirmed it is supporting the woman's family and is in contact with local authorities.