The accident took place in Lalbakaiya River, Chief District Officer of Rautahat Govinda Prasad Rijal told Xinhua.
According Xinhua, Rijal said that they have yet to find out the exact number of people aboard the boat.
According to him, the incident occurred when the boat reportedly hit a pillar of an under-construction bridge and toppled.
"We have already rescued 15 people so far and search operation is underway in coordination with police, army, and locals," Rijal said from the crash site, which is located 110 km southeast of the capital Kathmandu.
Due to rainfall, rivers in Nepal have gone swollen over the past weeks.