The accident took place in Jajarkot district when the bus carrying more than 60 people, passing through rough terrain, skidded off the road and plunged down.
Police said the bus was heading towards Khara from Khalanga when the incident occurred at Dhangaredanda, the Kathmandu Post reported.
At least 24 people were killed in the accident and as many as 41 were injured, police said.
The injured were receiving treatment at the District Hospital in Jajarkot.
DSP Bhabesh Rimal said that the accident might have occurred due to over-speeding.