The Tara Air plane took off from the tourist town of Pokhara, some 125 km west of capital Kathmandu, headed towards Jomsom, about 80 km to the northwest, the officials said. Tara Air mainly flies Canadian-built Twin Otter turboprop planes.
"One search helicopter returned to Jomsom due to bad weather without locating the plane," the Civil Aviation Authority of Nepal said in a statement.
"Helicopters are ready to take off for search from Kathmandu, Pokhara and Jomsom once weather conditions improve. Army and police search teams have left towards the site."
The airline said the plane was carrying four Indians, two Germans and 16 Nepalis, including three crew. Seven of the passengers were women, it said.
The plane lost contact with the control tower five minutes before it was due to land at Jomsom, a popular tourist and pilgrimage site, an airline official said on condition of anonymity.
The country's weather office said there had been thick cloud cover in the Pokhara-Jomson area since the morning.
Police official Prem Kumar Dani said a land rescue-and-search team had been sent to the area near Mount Dhaulagiri, the world's seventh-highest peak at 8,167m.
Nepal, home to eight of the world's 14 highest mountains, including Everest, has a record of air accidents. Its weather can change suddenly and airstrips are typically sited in difficult-to-reach mountainous areas.
In early 2018, a US-Bangla Airlines flight from Dhaka to Kathmandu crashed on landing and caught fire, killing 51 of the 71 people on board.
In 1992, all 167 people aboard a Pakistan International Airlines plane were killed when it ploughed into a hill as it tried to land in Kathmandu.
Photo: YUNISH GURUNG Caption: Family members and relatives of passengers on board the Twin Otter aircraft operated by Tara Air, weep outside the airport in Pokhara on May 29, 2022.