The victim was sent to hospital by air ambulance and police said shortly after 11am that she was still receiving medical care.
“She is seriously injured but stabile and confirmed to be out of critical condition,” police spokesman Petter Sandell said.
A 17-year-old boy who is also a student at the school has been arrested, police said.
A number of witnesses saw the stabbing, which took place within the school and was reported to police just after 8am.
“Police were on the scene six minutes after the message came in, and have arrested and taken control of whom we assume is the perpetrator,” Agder Police spokesman Bård Austad said earlier in the day.
The boarding school is operated by the Evangelical Lutheran revivalist movement Indremisjonsforbundet. It serves 61 students between the ages of 16 and 17.
“Currently, we know little about what has happened but there has been a stabbing between two students inside the dormitory,” school principal Steffen Røykenes told Fædrelandsvennen.
“The incident occurred just before the start of school. There are now quite a few police officers here who have started their work. We are taking care of our students as well as we can and the municipal crisis team is involved,” he added.
The incident comes a week to the day after a 14-year-old boy and a 48-year-old woman were stabbed to death on the grounds of a primary school in nearby Kristansand.