A sport utility vehicle carrying 20 people fell 200 metres down a cliff in Kalikot district, but one passenger managed to jump off the vehicle.
"Most of the injured are in serious conditions," Govinda Prasad Chaudhary, spokesperson for district police, told Xinhua news agency.
He noted that a Nepal Army helicopter had reached the site and that poor road conditions and overload could have resulted in the accident.
Two traffic accidents occurred in Nepal's Surkhet and Chitwan districts on Friday, leaving nine dead and 35 others injured.
Hundreds of people lose their lives in traffic accidents in Nepal each year.