The suspension bridge over the Bheri River in the Surkhet district, some 320 kilometers (200 miles) west of the capital, Kathmandu, collapsed while over 400 people were crossing it.
Local media said the people had been on their way to attend a full moon festival celebrating the end of the rice harvest.
Police, troops and locals have so far pulled 15 dead bodies from the river and rescued 32 people - 20 women and 12 men.
Bheri, one of Nepal's largest rivers, has a depth up 25 meters (82 feet) at the site of the disaster.
Around 200 of those who fell into the river reportedly managed to swim to safety. The ongoing rescue operation is being hampered by extremely cold water and the river's strong current. A source involved in the search said that the chances of finding more survivors were slim.
"We have no numbers [of those missing]," a police officer said, adding that the missing were mainly women and children.
