The accident occurred as the Twin Otter airplane on a flight from Pokhara skidded off the runway while trying to land at Jomsom airport in a mountainous region and crashed into the Kali Gandaki river, Rhishikesh Sharma, an official at the Civil Aviation Authority of Nepal said.
Police said the wheel of the plane skidded off the runway and veered toward the right and crashed on the river bank.
Rescuers pulled the injured passengers and crew from the plane.
Seven people including two Japanese, three crew members and two Nepalese were among those seriously injured in the incident.
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There were eight Japanese, 11 Nepalese including an infant and three crew members on board the NA-9NABO state-owned Nepal Airlines aircraft.
The accident site is located in a mountainous region, 350 kilometres north-west of Kathmandu.
The injured passengers are undergoing medical treatment at Manipal Hospital and Gandaki Hospital in Kaski district.
The cause of the accident is not yet known though strong mountain winds could be the reason.
Fifteen people were killed last May when a plane crashed while trying to land at the same airport.