The swirling floodwaters have even crossed into neighbouring India, submerging farmland and hundreds of villages.
At least 160 people are reported to have been killed in floods and landslides following days of torrential rain in both Nepal and northern India.
In Nepal, officials said at least 101 people were known to have died after rescuers found four more bodies. More than 130 are still missing.
In northern Indian states severe flooding left at least 60 dead and villages marooned.
Jhanka Nath Dhakal, of Nepal’s National Emergency Operation Centre, said four helicopters with food, emergency supplies, medicine and medical workers had been sent to villages in the west of the country.
Rescuers were also attempting to reach the villages by road, but most highways and rural roads are not passable.
Thousands of people have been left without shelter and cut off from the rest of the country since Thursday in ten districts in west Nepal.
Much of the area is farmland where the villagers are poor and live in mud and straw huts that are easily washed away.
Authorities fear the lack of clean drinking water, food and sanitation could lead to outbreaks of cholera, dysentery and encephalitis. Mr Dhakal said the government was trying to send medical teams to the villages to prevent the spread of disease. They are also distributing tents and plastic sheets to make temporary shelter.
“We are concerned about a possible outbreak of cholera because of all the dead bodies and livestock lying underwater,” he said.
Cholera is spread by drinking water contaminated by the faeces of people infected with the disease, which can kill within hours. It causes severe diarrhoea, vomiting and stomach cramps.
“We are on alert to make sure people don’t consume contaminated water, now or after they return to their homes over the coming week,” Mr Dhakal said.
National disaster management chief Yadav Prasad Koirala said authorities had “mobilised health workers to set up camps and provide people with clean drinking water and dry food”.
Alok Ranjan, chief secretary of Uttar Pradesh, said: “The flood situation arose following heavy downpours in Nepal, which led to overflowing rivers which originate in the Himalayan region including Tibet and Nepal.”
Earlier this month, a massive landslide covered an entire village near Kathmandu, killing 156 people.
People in the worst-affected villages were being evacuated yesterday to relief camps set up in government and school buildings, Mr Ranjan said.
Several rivers through Uttar Pradesh overflowed after water was released from dams located in Nepal, he said.
Heavy deforestation over the past few decades has made the area more vulnerable to landslides.