According to reports, more than 70 people have been killed in the country and the FCO confirmed there had been a “displacement of people, injuries and deaths”.
Road and airport closures are also affecting local transport links.
The FCO said: “You should plan travel in advance and contact your tour operator, the tourist police or the Nepal Tourism Board for further safety advice.
“Make sure any vehicle you travel in is equipped to deal with the risk of landslides (e.g. winches, ropes).”
The monsoon season normally runs from June to September and recent monsoon rains have the caused widespread flooding in Nepal.
Search and Rescue operations are underway in the most affected districts (Sunsari, Morang, Jhapa, Saptari, Sarlahi, Banke, Rautahat, Chitwan, Nawalparasi, Bardiya and Kailali).
Check the Meteorological Forecasting Division for latest updates and the Department of Hydrology and Metrology for flood forecasts.
In India, heavy monsoon rains continue to affect north Bengal and Assam.
Train lines have been affected by flooding, leading to disruption of train services and roadways.
“If you’re travelling to or in north Bengal or north-east India, monitor the local and international weather updates, follow the advice of local authorities and your travel company,” said the FCO.