A French woman has been injured by a polar bear that entered her camp in the Svalbard archipelago in Norway's Arctic, but her injuries are not life-threatening, authorities have said.

The woman, whose identity has not been disclosed, was part of an expedition of 25 people who were camping outdoors on the territory, which is just over 1,000 kilometres from the North Pole.

"A bear entered a camping area this morning around 8.30am and injured a French woman in the arm," said the head of the local police, Stein Olav Bredli.

"Her life is not in danger," he added.

The woman was evacuated by helicopter to a hospital in Longyearbyen, the archipelago's main town.

"It's a woman in her forties who has been lightly injured," said spokeswoman for the hospital authorities, Solveig Jacobsen.

The exact circumstances of the incident have not been disclosed.

"Shots were fired at the polar bear, who was scared off and left the scene," Mr Bredli said.

The animal was later located and put down, due to the extent of its injuries.

In Svalbard, it is mandatory to carry a rifle outside urban areas in case of an encounter with a polar bear. Males can weigh between 300 and 600 kilos, while females are about half that size.

A tally from 2015 put the number of polar bears on Svalbard at around 1,000. The animals have been a protected species since 1973.

Around 300 of them live in the archipelago year-round. Some have returned to the western part of the territory - the most inhabited area - where they were decimated when they were still allowed to be hunted.

Six people have been killed in polar bear attacks on the archipelago since 1971, the most recent in 2020 involving a 38-year-old Dutchman.

According to experts, shrinking sea ice caused by global warming is depriving polar bears of their preferred food, seals, pushing them to approach populated areas in search of other sources of nourishment.