The woman's condition was "serious but stable", Stockholm police spokesman Lars Bystroem said. She was detained on suspicion of destroying public property, a crime punishable by up to eight years in jail.
The train slammed into a three-storey building in the upscale Saltsjoebaden neighbourhood but no other injuries were reported.
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It was unclear why the woman stole the train from a Stockholm depot.
"The train was wrecked," Stockholm Public Transport spokesman Jesper Pettersson said.
Travelling at 80 kilometres (50 miles) per hour, it bolted off the tracks when it reached the end of the line and hurtled 25 metres in the snow before crashing to a final halt, according to train operating company Arriva.
The woman, born in 1990, had worked for a cleaning company contracted by the transport group "for a few months, with good results," Arriva spokesman Tomas Hedenius said.
Driving the train was "doable" for most people, as long as they had the key, he added.
