“After more than seven days in the extreme weather conditions of a glacier region, there is no longer any hope of survival for Karl-Erivan Haub,” the group said in a statement issued on behalf of the magnate's family.
It added that a multinational search for the 58-year-old had been called off.
Haub is the boss of Germany's sprawling Tengelmann retail group, which owns a number of chains and other businesses, 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.
Haub, a seasoned alpinist, had gone skiing solo but the alarm was raised when he did not show up for an appointment at his hotel in Zermatt. Swiss and Italian emergency teams have been combing the region around
Switzerland's iconic Matterhorn peak, with helicopters flying over the area while experienced rescuers have carried out foot searches.
But the search area covered thousands of hectares and operations on the Italian side were also hampered when a wave of harsh weather struck.
Swiss media reported that Haub had taken the ski lift at the Klein Matterhorn on Saturday at around 8:30 am (0630 GMT), and had set off at an altitude of 3,800 metres (12,470 feet) on the glacier-covered mountain — the
highest in Europe reachable by cable car.
Haub was training for the Patrouille des Glaciers, a gruelling race across the Alps organised every two years by the Swiss army and due to take place on Tuesday (April 17).
The race, billed as the world's toughest, was conceived on the eve of World War II, as neutral Switzerland prepared to defend the country's borders.
It was the brainchild of two captains from the 10th Mountain Brigade — a force tasked with protecting the southeastern Swiss Alps — who were looking for ways to hone their troops' skills.
Haub had participated twice in the competition that combines skiing and climbing. But rescuers believe that he had an accident during his solo practice run.
Tengelmann said efforts would be made to recover Haub's body for burial and that his family would bear all costs towards the search.
“This misfortune is a terrible and unbelievable tragedy for the Haub family as well as for the whole company,” said Tengelmann group spokeswoman Sieglinde Schuchardt.
Haub's disappearance came just a month after the death of his father Erivan Karl Matthias Haub, 85, who ran the company from 1969 to 2000.
The Tengelmann Group, a family-owned business, employs around 80,000 people worldwide. It said its revenues for the financial year of 2016 reached 9.0 billion euros.