71 passengers were on-board.
Police officials have said that at least 38 killed, 23 injured and 10 people still unaccounted for. Airport was closed for all arrival and departures.
Director General of Civil Aviation Authority of Nepal Sanjiv Gautam said the plane lost control when it attempted to land on the runway.
"The aircraft was permitted to land from the southern side of the runway flying over Koteshwor but it landed from the northern side," said Gautam, adding that the aircraft might have sustained technical glitches.
"We are yet to ascertain the reason behind the unusual landing," he said, news agency IANS reported.
Nepal Police spokesperson Manoj Neupane said the bodies of 31 passengers were recovered at the site and nine others succumbed to their injuries in hospitals. The plane, with 71 on board, was flying from Dhaka to Kathmandu, reported news agency.
The 78-seater Bombardier Dash 8 aircraft veered off the runway and caught fire while landing at 2.20 p.m., said TIA spokesperson Prem Nath Thakur.