The aircraft – said to belong to Agni Air – crashed as it tried to land at Jomsom airport, a key trekking hub.
Reports said a number of people had survived the crash but police reported at least nine deaths. Several Indian nationals were said to be on board.
Aviation accidents involving small aircraft are not uncommon in mountainous Nepal.
Last year 19 people were killed when a plane carrying tourists to view Mount Everest crashed outside Kathmandu.
“The plane was about to land at Jomsom airport. It hit a muddy slope and the plane is now buried in the side of the hill,” police spokesman Binod Singh told the AFP news agency.
The Agni Air 9N AIG was carrying 18 passengers and three crew members, and had been travelling to Jomsom from the city of Pokhara.
Reports say at least four survivors were taken to hospital in Pokhara for treatment.