The bus rolled some 100 meters (330 feet) from the highway and plunged Monday in the Trishuli river about 80 kilometers (50 miles) west of Katmandu, the capital.
Six bodies were pulled from the wreckage and three people died on the way to the hospital. Rescuers were able to pull seven more bodies from the swollen river later in the day.
It was not clear how many people had been on the bus, but rescuers continued to search the river for missing passengers. The river was flooded by the heavy monsoon rainfall, making the search difficult.
Police are investigating the cause, but it was raining heavily at 4 a.m. when the accident occurred.
At least 39 people were killed Sunday in another bus accident in Nepal, a mountainous nation where roads and vehicles are often poorly maintained.