The Norwegian Broadcasting Corporation reported that the group were with the British Schools Exploring Society.
The governor’s office in Svalbard district confirmed four people were in hospital and the bear had been killed.
The attack at Von Postbreen, about 25 miles (40km) from Longyearbyen, took place early on Friday.
Polar bears are, along with the grizzly bears of Kodiak Island, Alaska, the largest living predators on land.
They are also considered to be one of the few wild species that will actively hunt humans.
However, the chance to do so occurs rarely, due to the extreme isolation of their Arctic habitat.
The four people injured in the mauling were flown to Longyearbyen hospital and are due to be airlifted to a hospital in Tromsoe, the governor’s office spokeswoman said.
“We got a call via satellite phone from a British group of campers that there had been a polar bear attack and that one person was dead and that others were injured and they needed assistance,” she said.
“There are no roads in the area of the Von Postbreen glacier where the incident happened so we scrambled a helicopter.”
The British Schools Exploring Society’s (BSES) head office in London would not confirm that they were involved, but said their chairman would make a statement later.
BSES Expeditions is a youth development charity that organises scientific expeditions to remote areas to develop teamwork and a spirit of adventure.