Karl-Erivan Haub, heir to the Tengelmann retail empire, disappeared in the Alps at the weekend.
The 58-year-old, who has been described as an experienced skier and mountaineer, was training for a ski race when he vanished on the Matterhorn, which straddles the border between Switzerland and Italy.
Mr Haub’s family raised the alarm after he failed to return to his hotel on Saturday afternoon, according to Swiss newspaper Blick.
Adriano Favre, head of the mountain rescue services in Italy’s Aosta valley, was quoted by the newspaper as saying that bad weather and a high avalanche risk on the Italian side of the border had hampered the search effort.
Mr Favre said a six-person team had to interrupt their search on Tuesday.
He added that Mr Haub was skiing alone and because the area where he disappeared features glaciers, it is possible he could have fallen into a crevasse.
A Swiss police spokesman in Valais said rescue teams have been deployed on both sides of the border.
“He still hasn’t been found. The search is restarting today,” said Luca Bulgarelli at the Alpine rescuers’ office in Aosta.
“The weather is bad. There are clouds, but it’s not windy.”
Mr Haub – who was born in the US – and his brother Christian have spearheaded the company since 2000.
The family has an estimated fortune of more than €3bn.
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Mr Haub’s father, Erivan Haub, died last month on his ranch in Wyoming.
Tengelmann’s main businesses are the DIY store Obi and clothing shop KiK, while it also has large stakes in the supermarket chain Netto and online retailer Zalando.