At least eight people are reported to have been killed and 31 are missing after the floodwater swept through, according to state media.
The Friendship Bridge in Rasuwagadi, which connects Nepal with China 12 miles north of the capital Kathmandu, was destroyed by the water masses early on Tuesday.
Several houses and trucks were also swept away in the flood that came as a result of heavy monsoon rains.
People who were stranded have been able to be picked up by a military helicopter.
Monsoon rains that start in June and end in September often cause severe flooding in Nepal, which disrupts infrastructure and endangers lives.
