The injured people were brought by helicopter to Kathmandu and are being treated in two hospitals, Home Ministry official Chiranjivi Nepal said.
The bus veered off Arniko highway and rolled about 500 feet. Police were still trying to determine the cause. The highway is wide enough for two vehicles to pass but has sharp turns and no guard rails.
Parts of the bus, bodies and luggage were scattered on the forested slopes below the highway. Army and police rescuers were combing the slopes near Deurali village, 50 miles east of the capital.
Bus crashes are generally blamed on poorly maintained roads and vehicles in Nepal. Much of the crashes happen during the rainy monsoon season that begins in June and ends in September.