The flight, carrying 71 passengers and crew, crashed while landing at Kathmandu's Tribhuvan airport.
Survivors said they heard a loud bang and that the plane shock violently. Witnesses described chaos at the scene with people crying inside the aircraft.
The cause of the crash remains unclear, and an investigation is underway.
It is the worst aviation disaster to hit Nepal in many years.
'A loud bang'
The plane, which was flying from the Bangladeshi capital, Dhaka, was a Bombardier Dash 8 Q400 turboprop and was 17 years old. It was being operated by Bangladeshi airline US-Bangla.
"All of a sudden the plane shook violently and there was a loud bang," one of the survivors, Basanta Bohora, told reporters from his hospital bed. "I was seated near a window and was able to break out."
Basanta Bohora, who escaped the plane, is recovering in hospital
"The plane was going up down, right and left, up down. So I thought that was some air traffic only," Sanam Shakya, another one of the 22 survivors, told AFP.
"But I came to know that the aircraft had a problem only when it forcibly landed."
Shradha Giri, who on board a plane on a nearby runway with her daughter, told the BBC: "There was a lot of chaos out there, lot of security personnel running towards it, a lot of ambulances and fire trucks approaching the site where it had crashed."
"It was traumatising just to be with my little girl out there and yeah, everybody was shaken up because just something like that to happen in front of your eyes."
"The aircraft was burning," photojournalist Saroj Basnet told the BBC. "I was there around 15 minutes after the crash and the people were crying inside the aircraft."
It is still not clear what caused the crash. While the airline blames air traffic control, the airport says the plane landed from the wrong direction.
A recording of the conversation between the pilot and air traffic control minutes before the crash suggests some misunderstanding over which end of the sole runway the plane was cleared to land on.
A dangerous airport
A Retired Air Force Air commodore in Bangladesh, Iqbal Hossain, described to the BBC the challenges for pilots landing at Kathmandu.
"There is a mountain right behind the end of the runway.
"Every aircraft - while landing - has to maintain clearance from the mountain, and as soon as the pilot passes the mountain he has to do a very quick descent."
"There is some plain land on the left side of the runway but on the right side there is a deep gorge, so if the plane skids off the runway then it will fall into the gorge. It is among the 10 most dangerous airports in the world."
There have been many aviation incidents in Nepal.
Monday's crash was the deadliest since a Pakistan International Airlines plane crashed in 1992, killing all 167 on board.