Nepalese police said they had so far identified nine of the bodies.
The Chinese embassy in Nepal said a one of its citizen was among the dead, external, citing local police reports, though this has yet to be confirmed by Nepalese authorities.
Among the injured is a Chinese national and a New Zealander, Nepalese police said.
All the injured had been taken to hospitals in the capital, they added. Children were among those onboard.
Multiple teams were sent to the site, including police units, the army and a rescue team of divers, authorities said.
Police spokesman Abinarayan Kafle said 17 people died at the scene, with two more dying while receiving treatment, BBC Nepali reported.
Road accidents are relatively commonplace in Nepal, due to a range of factors including poor road maintenance and narrow paths in mountainous areas.
In 2024, at least 14 people died after a bus travelling from Pokhara to Kathmandu fell into the Marsyangdi river in the Tanahun district.
“We are supporting the family of a British man who has died in Nepal and are in contact with the local authorities,” a Foreign Office spokesman told the BBC.
Nepal is a popular destination for many international visitors, especially climbers, who travel there to access a key section of the Himalaya mountain range that includes Mount Everest.
Home to eight of the world’s tallest peaks, mountaineering is a significant source of revenue for the country – in 2024, climbing fees brought in $5.9m (£4.4m).