The bus with some 70 people on board skidded off the road and fell some 100 metres down into the Karnali River at Siyala of Dailekh district, 700 km west of Kathmandu, according to the police.
The bus was heading towards Surkhet from Kailali district.
Four people have been confirmed dead while 40 sustained injuries, police said.
A police team has been dispatched to the accident site and the rescue operation is underway.