The incident occurred as the plane - a Twin Otter belonging to Summit Air - with registration 9N-AMH skidded off the runway while preparing to take off and hit helicopters parked 30-50 metres from the runway, the Kathmandu Post reported.
Seven people, including the country's tourism minister, were killed in February when a helicopter crashed in the hilly east.
It's believed a small plane crashed into a helicopter while taking off from an airstrip.
"Two people died on the spot and the third one died while undergoing treatment in a hospital in Kathmandu", airport official Pratap Babu Tiwari told Reuters.
The other pilot from the plane and the helicopter pilot are among the injured - they were airlifted to Kathmandu.
Nepal police spokesman Uttam Raj Subedi was cited by New Zealand news service Stuff as saying that the dead included a pilot of the plane and two police officers standing near the parked helicopter.
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Mr Thomas said there were "a few little things that were off-nominal but really for a first flight it was spot on". Test pilot Evan Thomas said "the flight itself was smooth, which is exactly what you want a first flight to be".
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"We are not sure about the cause of the accident".
A civil administrator, Narendra Kumar Lama, said the four passengers and a flight attendant on the plane were safe.
Lukla airport, also known as Tenzing-Hillary airport, is the gateway to Mt Everest.
Tenzing-Hillary Airport is known as the gateway to Everest and is regarded the world's most risky because of its hard approach and short runway.
The Tenzing-Hillary Airport sits at an elevation of just over 9,000 feet.