Kamala Balan river, swelled by the flood waters of its tributaries, breached the embankment near Ghanshayampur in Darbhanga.
The flood waters then submerged over a dozen villages, affecting thousands of people.
In other parts of the state, after heavy donwpour pushed up the water level of Kosi, Gandak and Bagmati rivers, hundreds of villages have been inundated and thousands were marooned.
Vayasji, principal secretary of state disaster management department, told IANS that that the flood situation is grim.
"We have sounded a high alert as major rivers in north Bihar, especially the Kosi, Gandak, Kamla Balan and Bagmati, are in spate following heavy rains in their catchment areas in Nepal and are posing a threat of floods," he said over phone.
Vayasjit said that so far no casualty has been reported due to flood in the state.
In view of the situation in some areas, eight teams of the National Disaster Response Force (NDRF) and state disaster response force have been deployed in flood-hit districts.
Vayasji said he has asked for five additional NDRF teams from the central government.
The state disaster management department has asked people living in low-lying areas to move to higher ground, he said.
Reports reaching here said hundreds fled their homes after water entered their villages in Supaul, Saharsa, Bagha, Gopalganj, Madhubani, Sitamarhi, Khagaria, Darbhanga and Madhepura.
A water resource department official said: "Water entered these villages after levels rose in all the major rivers following heavy rain in the state and the catchment areas in Nepal."