The calamity ocurred when a barrage in neighbouring Nepal burst its banks after monsoon rains, causing the river Kosi to change its course, shifting 120km eastwards.
More than 5665 cumecs of water entered the state of Bihar through the breach embankment of Kosi, affecting 2.5M people in 15 state districts.
Aid workers are struggling to reach some 50,000 people marooned in the area, as many roads and railways have been inundated.
Humanitarian aid organisation ActionAid says that water levels rose by 1m on the national highway that connects Delhi with Bihar's capital Patna (NH31). Only large vehicles are able to traverse the road.
The Ministry of Home Affairs announced that the Army is having difficulty transporting boats to rescue people in the district as the only available route, a national highway between Maheshkut and Saharsa, has been overflown with floodwater.
Water and electricity supply in many districts has been cut off and railway tracks at several places have been submerged under deep water.
"We anticipate that things will get worse since the broken embankment is widening. It is likely that more villages will be marooned in the coming week," said ActionAid Bihar regional manager Vinay Ohdar.
The Indian government has been criticised for not sufficiently protecting the region against a known threat. The Kosi river suffered devasting flooding in 1954, triggering a proposal to build a 239m dam with 50km of Nepal, but the project was shelved.
Repair work on the Kosi river barrage and embankment system has been a topic of debate for years, since it was built as a temporary measure in the 1950s.
Commenting on the catastrophe, Atkins director A Sreenivasa Murthy, based in Bangalore, said: "Most of the work needs to be done in Nepal rather than India. It is basically an international problem between the two countries."