Video and photographs from the scene showed flight 2276, a Boeing Co 777 bound for London Gatwick, engulfed in flames and thick black smoke. Emergency slides were deployed from the aircraft.
According to preliminary information, the plane experienced a left engine fire on takeoff, said Ian Gregor, a spokesman for the Federal Aviation Administration's Pacific Division.
McCarran International said the fire had been put out, and published a photo of the plane with its charred fuselage. It said flight operations continue on its three other runways.
A spokeswoman for British Airways, which is owned by IAG, said safety is always the airline's priority and the airline is looking after customers.
Witnesses say even the pilot looked shaken up.
Jacob Steinberg, a reporter for Britain's Guardian newspaper, who was on board the flight, said on Twitter that he was initially told to stay seated, but there was panic when smoke appeared in the cabin.
Steinberg said the shaken pilot later joined the passengers inside the terminal and told them the fire was caused by a catastrophic failure of the engine.
Seven passengers were taken to hospital with minor injuries.
