The small Shangrila Airlines Twin Otter aircraft was travelling from Jomsom to the tourist town of Pokhara, about 200 kilometres (120 miles) west of the capital, Kathmandu.
The dead include 13 Germans, one Briton and one US citizen, as well as three Nepalese crew. There were no survivors. All 18 bodies have been recovered.
Later on Thursday, a bus plunged 60 metres (200 feet) into a swollen river 110 kilometres (68 miles) west of Kathmandu - at least 45 people are missing feared dead.
The bus was travelling from the capital to a hill town when the driver lost control as he tried to overtake another vehicle.
Heavy rain has hampered the search for the missing bus and passengers.
Monsoon rains
In the earlier incident, the Twin Otter plane crashed after disappearing into a cloud and vanishing from radar screens at about 1000 local time (0415 GMT), just 20 minutes from its destination.
Nepal air record
July 2002 - Twin Otter crash kills four near Surkhet
Nov 2001 - royal family member among six dead in helicopter crash
September 1999 - 15 dead in crash near Kathmandu
July 1999 - cargo plane crash kills five
Officials say bad weather may have been a factor in the crash. Rescue helicopters have been sent to the scene.
Nepal and neighbouring countries have been battered by torrential monsoon rains which have led to a series of landslides and floods over the last two months, many in remote areas of the country.
On Wednesday, a landslide in the remote Ramechhap district in the east of the country swept away a village and killed more than 100 people - one of the worst disasters caused by monsoon rain in a decade.
Pokhara and Jomosom are both popular centres for trekking holidays into the Himalayas. The plane's route took it close to Annapurna, one of the world's highest mountains.
Mixed record
There are more than a dozen private airlines in Nepal, which is mountainous and has a poor road network.
The BBC's Adam Mynott - reporting from Delhi - says the airlines have a mixed record.
On 17 July a Twin Otter plane belonging to the private Skyline Airlines crashed, killing all four people on board.
The DeHavilland Twin Otter, a highly manoeuvrable aircraft which can be flown slowly and in tight circles, is commonly used for flights in jungles, deserts, mountains and the polar regions.