Everyone on board is feared dead, Nepali Tourism and Aviation Minister Ananda Pokharel said. The official said a few bodies have been found but are unrecognizable.
The Twin Otter plane took off Wednesday morning from the city of Pokhara. It was scheduled to land in the town of Jomsom, Tara Air spokesman Bhim Rai said.
The total flight time was supposed to be 19 minutes, but contact was lost eight minutes after takeoff.
Residents in Nepal's Myagdi District saw flames shooting up from a forest and called security officials, Pokharel said. Authorities arrived and found the plane's wreckage.
Eighteen passengers and three crew members were on the plane, Rai said. The passengers include two foreigners -- one Chinese and one Kuwaiti.
The cause of the crash has not been determined.
Rai said the weather Wednesday morning was clear when the plane took off. He said the Twin Otter plane was new, imported from Canada last September, CNN reported.
Pokhara, where the flight originated, is one of the most popular tourist destinations in Nepal. Jomsom is the gateway for one of the most popular Himalayan trekking routes.