The Twin Otter aircraft took off from the western town of Pokhara at 9:55am (0410 GMT) but soon lost contact with air traffic control.
“A domestic flight bound for Jomsom from Pokhara has lost contact,” Sudarshan Bartaula, spokesman for Tara Air, told AFP.
He said there were 19 passengers on board and three crew members.
Phanindra Mani Pokharel, a spokesman at the Ministry of Home Affairs, said two helicopters have been deployed for a search operation. But he said visibility was low.
“The bad weather is likely to hamper the search operation. The visibility is so poor that nothing can be seen,” Pokharel said.
Jomsom is a popular trekking destination in the Himalayas about 20 minutes by plane from Pokhara, which lies west of Kathmandu.