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Rescuers were scouring the crash site near Pokhara International Airport on Sunday and expected to find more bodies, said Tek Bahadur KC, a senior administrative officer in Kaski district.
The plane was carrying 68 passengers and four crew members, the Kathmandu Post newspaper reported, quoting a spokesman for Yeti Airlines.
Prime Minister Pushpa Kamal Dahal said the plane was flying from the capital, Kathmandu, to Pokhara and he urged security personnel and the general public to help with the rescue efforts.
Pokhara, located 125 miles (200km) west of Kathmandu, is the gateway to the Annapurna Circuit, a popular hiking trail in the Himalayas.
Images and videos shared on Twitter showed plumes of smoke billowing from the crash site as rescue workers and crowds of people gathered around the wreckage of the aircraft.
Nepalese soldiers were also involved in the rescue efforts at the crash site.
The cause of the crash was not immediately clear.
Nepal has had a patchy air safety record.
Last year, 22 people died when a plane crashed on a mountainside in Nepal.
In 2018, a US-Bangla passenger plane from Bangladesh crashed on landing in Kathmandu, killing 49 of the 71 people on board.