The woman's condition is critical, according to Japanese media.
The accident occurred on Monday, when the woman and two other people began climbing Mount Fuji early in the morning. As they were about to ski back around 3 p.m., something happened that caused the Swedish woman and a New Zealand man in his 50s to lose their way and slide down the side of the mountain.
A rescue team searched for the two missing people for several hours but only found them shortly before 11 p.m. It was not until the next morning that the rescue team managed to transport them by helicopter to a hospital about ten miles south of Tokyo.
The Ministry of Foreign Affairs said it was aware that a Swedish woman was involved in an accident in Japan.
