Three survivors apparently swam to safety, but rescuers by late morning had not found any trace of the buses, which likely were submerged and swept downstream in the Trishuli River.
Nepal's rivers generally are fast-flowing due to the mountainous terrain. Heavy monsoon downpours in the past few days have swollen the waterways and turned their waters murky brown, making it even more difficult to see the wreckage.
Home Minister Rabi Lamichhane told parliament 51 passengers were missing and more than 500 rescue personnel have been assigned to the search operation.
Elsewhere in the country, 17 people have died and three more people were injured due to landslides in different districts in the past 24 hours, he said.
The buses were on the key highway connecting the capital to southern parts of Nepal when they were swept away around 3 a.m. near Simaltal, about 120 kilometers (75 miles) west of Kathmandu.
RHM/PR