On its Facebook page, the Santa safari tour operator Transun confirmed its employee's death on Saturday
The suspect -- the woman's 36-year-old Czech boyfriend -- fled on a dog-sled, sparking a manhunt involving police on snowmobiles, the daily Helsingin Sanomat added.
He was arrested after being spotted by a helicopter crew and taken to hospital suffering from hypothermia before being transferred to police custody, according to police and media.
The Briton, who has not been named, died from her wounds. The attack happened on Saturday in Kuttanen, which lies close to the Swedish border and around 150 kilometres (90 miles) north of the Arctic Circle.
On its Facebook page, the Santa safari tour operator Transun confirmed its employee's death on Saturday without providing further details.
"We are deeply saddened to confirm that a member of staff working for our overseas supplier Santa safari was discovered dead on the 3rd December.
"The thoughts of everyone at Transun go out to the family, friends and the Santa safari team," it said.
Due to the police investigation, there would be some disruption to planned tours, it added.