Police said the bus carrying 32 passengers plunged 70 metres (230 feet) onto a lower stretch of the winding road in Sindhupalchowk district, around 80 kilometres north-east of the capital Kathmandu.
"We have recovered the bodies of 12 passengers from the accident," police officer Prajwal Maharjan told AFP, adding that two others had died in hospital.
Four of the dead were children, traffic police added.
Three killed in road accidents
Some 18 passengers who were injured were taken to hospital, with officials unclear if the bus driver was among them or had fled the scene of the crash.
The passengers were returning from a pilgrimage to Kalinchowk Bhagawati, a popular Hindu temple located at a heigh of almost 4000 metres in the hills of Nepal's Dolakha district, around 140 kilometres east of Kathmandu.
The cause of the accident was not yet known, but police said reckless driving down the steep and winding road could have been a key factor.
Deadly traffic accidents are relatively common in the impoverished Himalayan nation because of poor roads, badly maintained vehicles and reckless driving.
At least 18 passengers were killed when a bus plunged into a gorge in central Nepal last month.
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