The climber was one of three from South Korea who arrived at the Hörnlihütte above Zermatt on Sunday, Valais cantonal police said in a statement.
The group were planning to tackle the 4,478-metre summit on Monday but made a reconnaissance trip along the exposed Hörnligrat ridge route on Sunday afternoon.
However, they struck bad weather during the sortie and were forced to spend the night on the mountain at an altitude of 3,900 metres.
At around 2pm on Monday afternoon, the group decided to move to a new location but one of the climbers fell while abseiling.
His body was later recovered by rescue services.
The two other climbers were uninjured.
An official investigation into the accident is now being carried. Formal identification of the body has not been carried out.
The Matterhorn ascent requires sure-footedness and excellent fitness. Over 500 people are estimated to have died while ascending or descending the mountain. Use of a guide is very highly recommended.