Officials said there were 71 people on board the US-Bangla Airlines turboprop plane from Dhaka when it crashed just east of the runway and skidded into a nearby football field.
Rescuers cut apart the mangled and charred wreckage of the upturned aircraft to pull people out, while other passengers were found buried under debris that scattered as the plane hit the ground.
"Forty people died at the spot and nine died at two hospitals in Kathmandu," police spokesman Manoj Neupane told AFP, adding another 22 were being treated in hospital, some in a critical condition.
Survivor Sanam Shakya, who climbed out of a window of the smouldering plane, said he didn't realise the aircraft was in trouble until it hit the ground.
"The plane was going up down, right and left, up down... so I thought that was some air traffic only. But I came to know that the aircraft had a problem only when it forcibly landed," the 33-year-old said from a hospital bed.
The cause of the crash was not immediately clear, but a statement from airport authorities said the plane was "out of control" as it came in to land.
"Meanwhile, the CEO of US-Bangla Airlines Imran Asif laid blame on Kathmandu's air traffic control, saying the controller "fumbled" the landing.
"Our pilot is an instructor of this Bombardier aircraft. His flight hours are over 5,000 hours. There was a fumble from the control tower," Asif told reporters outside the airline's offices in Dhaka.
An airport source, who spoke on condition of anonymity, said there may have been confusion between air traffic control and the pilot over which end of Kathmandu's sole runway -- referred to as 'Runway 02' and 'Runway 20' -- the plane was meant to land on.
A recording purportedly of the conversation between the controller and pilot has been published online. AFP could not independently verify the recording.
Eyewitnesses said the plane -- a Canadian-made Bombardier Dash 8 Q400 turboprop -- crashed as it made a second approach towards the airport, shuddering violently as it lost height before hitting the ground and bursting into flames.
"It should have come straight but it went in the other direction... then it crashed towards the field," said airport cleaner Sushil Chaudhary, who saw the crash.