Police said the bus drove off the Prithvi highway near the town of Gajuri, 120 kilometers west of the capital, Kathmandu, and fell a few meters into the river, TRT World reported.
The bus was partly submerged in the Trishuli River, but rescuers were able to pull out many of the passengers alive from the wreckage. The injured passengers were taken to hospitals for treatment.
The river had been swollen by continuous rainfall during the monsoon season.
It was unclear what caused the crash, but the rainfall has made roads slippery and visibility low on the curvy mountain highway.
AMK/PR