"Search teams on the scene are doing everything they can" to find 58-year-old Karl-Erivan Haub after his failure to return from a ski excursion Saturday, a company spokeswoman told AFP.
"My brother is a very experienced ski mountaineer, so despite the time that has passed since (his disappearance) we aren't giving up hope of finding him soon," Christian Haub, who jointly manages the Tengelmann group with Karl-Erivan, wrote in a letter to employees seen by German business newspaper Handelsblatt.
"Please cross your fingers for us to find my brother quickly," he asked.
"The family has made unlimited resources available to the search teams," mountain rescue leader for the Aosta valley Adriano Favre told Swiss newspaper Blick, "but in these conditions they're useless," pointing to bad weather on the Italian side of the mountains.
Haub set off at a height of 3,800 metres (12,470 feet) on the Klein Matterhorn, a glacier-shrouded peak that is the highest in Europe reachable by cable car.
Blick reported that he was training for the "Patrouille", a ski mountaineering race organized by the Swiss army slated this year for April 17th.
The Tengelmann group owns a number of retail chains and other businesses in Germany, including the Kik low-cost clothing stores and OBI home improvement outlets.
Its success has lifted the family into 265th place on Forbes magazine's global rich list, and 20th place in Germany.