The plane with 15 passengers and three crew on board lost contact with air traffic controllers shortly after taking off from the popular tourist town of Pokhara, airline officials and police said.
"The Nepal Airlines plane with 14 (adult) passengers took off from Pokhara airport at 1.30 pm and disappeared 15 minutes later," Nepal police spokesperson Ganesh KC told AFP.
A total of 18 people were on board, the 14 adult passengers, plus one infant and three crew, an airline spokesperson said.
"One of the passengers is from Denmark," spokesperson Ram Hari Sharma told AFP. The rest of those on board are from Nepal.
Heavy rain was hampering efforts to search for the plane, with two helicopters forced to turn back because of bad weather, Bimlesh Lal Karna, chief air traffic controller at the country's largest airport in Kathmandu, said.
"The weather was not bad at the time the plane went missing ... It worsened later on," Karna told AFP. "Two helicopters that were sent from Pokhara returned due to bad weather," he said.
"We are sending another one from Kathmandu," he added.
The state-run carrier was travelling from Pokhara to the town of Jumla, 353 kilometres west of the capital Kathmandu, when air traffic controllers lost contact with the pilot.
The incident again raises concerns about the Himalayan nation's aviation sector, which has come under fire from international authorities after a series of fatal accidents.
The European Union in December blacklisted all the country's airlines and banned them from flying to the EU.
Nepal, which counts tourism as a major contributor to its economy, has suffered a number of air crashes in recent years, which have usually been attributed to inexperienced pilots, poor management and maintenance.
A Chinese tourist and a local pilot were killed when an ultra-light aircraft crashed into a hill in the tourist town of Pokhara last October.
Last May, 21 people, including eight Japanese tourists, were hurt when a small plane skidded off an airport runway in northern Nepal.
In September 2012, 19 people, including seven Britons and four Chinese, were killed after a plane crashed minutes after taking off from Kathmandu, in an accident which the government blamed on a "panic-stricken" pilot.
At the time of the blacklisting last year, EU Transport Commissioner Siim Kallas said the country's safety record "does not leave us any other choice".
Government officials said the ban was "unfortunate" and came after months spent on upgrading safety measures and monitoring aircraft.
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