Officials at Kathmandu's Tribhuwan International Airport said the plane with 238 people on board was coming from Istanbul when the accident happened.
They say passengers had bumps and bruises but no serious injuries.
The runway was slippery after two days of rain and there was dense fog at the time. The plane was stuck in the grass and there was some damage to the front of the Airbus 330.
The plane on a seven-hour flight circled for half hour over Nepal before it made a second attempt to land.