The plane, operated by Sita Air, came down minutes after take-off from Kathmandu. Officials said it crashed into a river bank and caught fire.
Sixteen passengers and three crew were on board the twin-engine prop plane.
Police and aviation officials, however, said that seven Britons, five Chinese nationals and seven Nepali nationals were on the plane, including the three Nepalese crew.
The cause of the crash is not yet known, however the general manager of Tribhuvan International Airport, Ratish Chandra Lal Suman, said in a statement that the plane had struck a bird.
He said air traffic control contacted the pilot after noticing an unusual manoeuvre minutes after take-off. The pilot said his plane had hit a vulture, the statement said.
The plane had been heading for Lukla, the hub for trekking in the Everest region.
Police spokesman Binod Singh told the AFP news agency that “the pilots seem to have tried to land it safely on the banks of the river but unfortunately the plane caught fire”.
Images showed burning wreckage at the crash site and dozens of rescue and security personnel.
British mountaineer Alan Hinkes said he had taken the flight from Kathmandu to Lukla many times and that problems usually occurred at the Lukla end.
“The landing strip in Lukla is a bit like an aircraft carrier with a mountain at the end of it, with a 1,000ft drop at the end of the runway. Normally crashes happen at that end,” he said.
He added: “It is not the safest place to fly, I must admit, but it is what you have to do to get into the mountains.”
Aviation accidents involving small aircraft are not uncommon in mountainous Nepal.
In May, 15 people were killed when a plane crashed trying to land at an airport in the north of the country.
And in September 2011, 19 people were killed when a Buddha Air plane crashed during a flight to view Mount Everest.
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