The 26-year-old woman, who has not been named, was found stabbed to death in the village of Kuttanen in Finland on Saturday (December 3).
Lapland Police said her 36-year-old Czech boyfriend fled the area on a dog sled – launching a manhunt involving snow scooters and a helicopter.
He was later found by authorities in temperatures of -30C and taken to hospital.
Following treatment, he was taken into police custody on suspicion of killing the Briton, BBC News reports.
The pair had been seasonal workers in the region.
The woman, believed to be from Scotland, was employed by Santa Safari, which partners with Oxford-based tour operator Transun Travel to organise Christmas-themed excursions in Lapland.
A spokesperson for Santa Safari said: "We are deeply saddened to confirm that a member of the Santa Safari team was discovered dead on the December 3.
"We are all in shock from this tragic news and our thoughts go out to her family.
"Our team is working closely with the Finnish Police and relevant authorities to support the investigation that is now under way.
"It goes without saying that we will do everything we can to support the family and our staff at this incredibly difficult time."
A Police Scotland spokesperson said: "Police Scotland have been contacted by the Foreign and Commonwealth Office regarding the death of a British national in Finland and will continue to assist them as required."
A spokeswoman for the Foreign Office said: "We are supporting the family of a British national who died in Finland on December 3."
In a statement on its Facebook page Transun said: "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. We will do everything we can to support them at this difficult time."
