The two people involved, aged 73 and 77, were part of a group of 12 senior citizens on a ski touring trip from Säntis to Toggenburg, according to Appenzell Innerhoden police.
Immediately below the mountain cabin Alter Säntis one of the skiers slipped and fell, knocking into another a few metres below. Both ski tourers then fell 160-200 metres, causing the death of one.
Due to the foggy weather it was not possible to bring in a Rega helicopter, so rescuers had to take the cable car to Säntis and then descend on foot to the scene of the accident, said police.
Given the steep terrain it was a difficult rescue, but the injured person was eventually transported by cable car to the Schwägalp and then driven to hospital.
Säntis is the highest mountain in the Alpstein region, a popular place for hiking and ski touring, though it is known for its extreme weather conditions.
From the summit it's possible to see Switzerland, Germany, Austria, Liechtenstein, France and Italy at the same time.