The mountaineer was descending with his team on Tuesday after successfully summiting the 6,091-metre (19,983-foot) high Pisang peak in the Annapurna region.
His three other team members only realised that he was missing when they arrived at base camp, Manang district chief Bhim Kanta Sharma told AFP.
"The climber was reported missing on Tuesday evening and we have begun our search," Sharma said, adding that it was unclear where on the mountain he was.
"Rescue teams have been deployed in a helicopter as well as on foot, but rain and snow are making the operation difficult," he said.
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Two trekkers, from Japan and Korea, also died last week of suspected altitude sickness on their way down from Nepal's Everest base camp.
Every year hundreds of people from around the world travel to the Himalayas in Nepal for the brief spring climbing season, when conditions are at their best.
Mountaineering is a major revenue-earner for impoverished Nepal, home to eight of the world's 14 peaks over 8,000 metres.