All passengers and crew members on the domestic flight were reportedly safe.
An aircraft with a call sign 9N-AMM, which was flying from western city Nepalgunj, had runway excursion while landing at Kathmandu airport. It reached to the parking bay area after skidding off.
"All 66 passengers including two infants and three flight crew members onboard are safe and have been evacuated," Yeti Airlines issued a formal notice in social media.
According to the airport officials, the country's sole international airport remained closed following the incident and will resume after the removal of the aircraft from the spot.
All the incoming flights were transferred to other countries while the outgoing flights were halted.
The incident happened as Nepal has been witnessing heavy rainfall since early Friday morning.
Runway excursions are common in the airport's single 3-km-long runway. Since April, the TIA has been undergoing a runway upgrade program.
In March last year, an aircraft of US-Bangla Airlines crashed near the TIA runway, killing some 50 people.