Kim had finished scaling the 26,400ft Broad Peak before it is believed he fell into a crevasse.
Aged 57, his climb made him the first ever disabled person to reach the summit of all of the world’s tallest mountains.
An initial search has thus far failed to locate him, but a large operation is currently in the process of being planned.
As reported by the Korea Herald, Kim, who had to have all of his fingers amputated in 1991 when he suffered severe frostbite climbing in Alaska, reached the top of Broad Peak at the weekend as part of a small group’s expedition.
According to the Pakistan Alpine Club’s secretary Karrar Haidri, he is thought to have slipped then fallen as he descended the mountain’s Chinese side in poor weather conditions.