“There were 159 passengers and 13 crew on the flight,” McCarran International Airport in Las Vegas said.
It added that seven people on board the London-bound flight were treated for minor injuries.
The Federal Aviation Administration said the fire broke out in the left engine of the 257-seat Boeing 777 shortly after 4:00 pm (2300 GMT) and a probe was underway to determine the cause.
“Passengers deplaned on the runway using emergency slides and (were) bused to the terminal,” FAA spokesman Ian Gregor told AFP.
An AFP correspondent at the airport said the blaze was quickly put out by firefighters who rushed to the site within minutes along with other emergency vehicles. The plane was still parked on the runway by early evening.
Passengers described scenes of panic on the plane with one witness telling CNN “we heard a lot of screaming.”
Some of the passengers posted dramatic images and videos that showed plumes of smoke and flames engulfing the aircraft.
“Just got evacuated from our flight#BA2276 plane caught fire somehow omg,” passenger Dominic Worthington said on Twitter.
Jacob Steinberg, a reporter for Britain’s daily The Guardian who was on board the flight, said on his Twitter account that he was asleep as the plane was on the runway and came to a “crashing halt.”
“Initially told to stay seated, then shout of evacuate,” he said, adding that the flames had apparently melted some of the jet’s windows.
“They opened the back door and slide went down and smoke started coming in plane, followed by mad dash to front. A lot of panic,” he said.
Steinberg said the pilot later joined the passengers inside the airport terminal and told them the fire was caused by a “catastrophic failure of the engine.”
“The pilot looked pretty shook up to be honest,” he said. “Has been flying for years, don’t think he had ever seen anything like that.”
Paul Berberian, a passenger aboard another plane that was on the tarmac at the time of the incident, described watching in disbelief as the British Airways plane caught fire and smoke billowed from the fuselage.
A video shot by Berberian and aired on CNN shows the stricken plane’s passengers using evacuation slides and running away on the tarmac as emergency vehicles rush to the site to douse the flames.
“We were all glued to the side of the plane watching this unfold,” he said of fellow passengers on his flight.
‘Gathering more information’
McCarran Airport said traffic on runway number three, where the incident took place, had been suspended but flights were operating normally from the three other runways.
Passengers from the stricken plane were taken to a hotel near the Las Vegas strip for the night while awaiting another flight to their destination.
“We’re aware of the incident at McCarran Airport in Las Vegas,” Boeing said in a statement. “Our teams are currently gathering more information.”
British Airways had no immediate comment on Tuesday’s incident other than to say that it was looking after the passengers.
In 2014, a British Airways planed heading to Lyon, France, was forced to turn back to London’s Heathrow Airport after a witness saw flames “spitting” out of the engine on takeoff.