The 19-seat Yeti Airlines aircraft, which had taken off from the capital, Kathmandu, snagged its wheels on a security fence during its landing at Lukla airport, about 60km from Mount Everest, Mohan Adhikari, general manager of the Kathmandu airport, said.
The DeHavilland DHC-6 Twin Otter caught fire and came to a stop on the airport grounds, he said.
The Twin Otter is known for its ability to take off and land on short runways.
Adhikari said 19 people were on board the aeroplace, including 12 German, two Australian and two Nepalese tourists.
There were also three Nepalese crew members - a pilot, co-pilot and flight attendant.
The pilot was flown to Kathmandu and hospitalised in critical condition though Vijay Shreshta, executive director of Yeti Airlines, said his injuries were not believed to be life-threatening.
The 12 Germans were on a tour run by Munich-based Hauser Exkursionen.
Jumping-off point
The Lukla airport is little more than a runway carved into the side of the Himalayas at an altitude of 9,200ft.
It is an important jumping-off point for trekkers and mountaineers heading to Everest.
The runway ends in a steep drop of a few hundred metres.
A fog had descended on the airport just before the crash, Suraj Kunwar, who was at Lukla waiting for a flight, said.
"Suddenly there was a big bang, and flames came out of the plane," he said.
"All the passengers waiting for planes ran to help douse the flames, but the passengers were already dead."