Three passengers managed to escape and received treatment at a nearby hospital, according to city official Khimananda Bhusal, who told AFP on Friday that the trucks had between them at least 66 people.
The crash happened before sun along the Narayanghat-Mugling bridge, around 100km east of Kathmandu.
One van was traveling from southern Birgunj to Gaur in Rautahat region in southwestern Nepal, and the other was traveling to Kathmandu.
A pilot was killed when a stone struck his bus in a separate incident on the same road. He passed away while receiving care in a clinic.
Due to poor road construction, poor maintenance, and reckless driving, fatal crashes are frequent in the Himalayan state.
Almost 2, 400 people lost their lives on Nepal’s routes in the 12 month to April, according to government statistics.
In a January incident where a bus from Nepalgunj to Kathmandu fell into a valley, 12 people were killed and 24 were hurt.
As rains cause mudslides and floods across the mountainous region, path travel becomes more dangerous during the monsoon period.
Monsoon rains that occur in South Asia between June and September are both important for regenerating water resources and cause widespread death and destruction.
Although the snowfall is difficult to predict and varies widely, researchers claim that climate change is making the rain stronger and more unpredictable.
Since the rain first started in June, 88 people have died as a result of storms, floods, and lightning hits, according to authorities figures.