The Poland-made Skytruck overturned and caught fire after it overshot the runway after attempting to land, said Devendra Lamichanne, chief district officer for Bajura where the accident occurred.
It was carrying food supplies to the remote far west of the Himalayan nation, where road access is poor.
Poor weather forced the pilot to divert, but conditions were said to be good in Bajura and it is unclear why the plane crashed.
Rescuers put out the flames and pulled out those inside -- even cutting into the plane to remove one.
"The pilot died as he was being taken to the hospital. The other two are being treated," police official Sudam Rawal told AFP.
The accident comes three days after a cargo aircraft crashed at an airport near Mount Everest, killing the pilot and the co-pilot.
Two deadly plane crashes last year claimed at least 25 lives, the first when a passenger plane slammed into a mountainside and the second when a small aircraft crash-landed killing the two pilots.
Despite the risks, air travel is popular in Nepal, which has a limited road network.
All Nepal airlines are banned from flying to the European Union because their poor safety standards.
(Except for the headline, this story has not been edited by NDTV staff and is published from a syndicated feed.)