It was not clear how it slipped or the status of the people on board.
The Saurya Airlines plane was heading from Kathmandu to the resort town of Pokhara, AP reported.
Local media images showed smoke rising and plane wreckage scattered all over a ditch. A fire has been brought under control.
Tribhuvan International Airport, the main airport in Nepal for international and domestic flights, has been closed as emergency crew worked.
It is the monsoon rainy season in Kathmandu but was not raining at the time of the crash. Visibility was low across the capital, however.
Saurya Airlines operates the Bombardier CRJ 200 on domestic routes.
SD/
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