Another official told AFP that so far 20 injured had been taken to hospital.
Plumes of black smoke could be seen rising from the football pitch where the plane crashed, to the east of the runway at Nepal’s only international airport, in the capital Kathmandu.
“There were 67 passengers and 4 crew members” aboard the plane, said airport spokesman Prem Nath Thakur.
“Police and army are trying to cut apart the plane to rescue others,” he added.
Live footage posted on Facebook showed towering columns of smoke rising behind the runway, where another plane stood waiting on the tarmac.
Emergency vehicles appeared to be heading into the smoke as people watched from a distance or filmed on their mobile phones.
An official who spoke on condition of anonymity because of airport policy said the flight was arriving from Dhaka, the Bangladeshi capital. He said the plane appeared to have caught fire just before it landed and skidded to a stop in a field beside the runway.
US-Bangla is a private Bangladeshi carrier. An employee who answered the phone at the US-Bangla offices in Dhaka said no one was available to talk.
“I have no other details,” said the employee, who refused to give his name. “But a bad incident has happened.”
Nepal has suffered a number of air disasters in recent years, dealing a blow to its tourist industry.
Its poor air safety record has been blamed largely on inadequate maintenance, inexperienced pilots and substandard management.
In early 2016, a Twin Otter turboprop aircraft slammed into a mountainside in Nepal, killing all 23 people on board.
Two days later, two pilots were killed when a small passenger plane crash-landed in the country’s hilly midwest.