Several passengers and crew suffered minor injuries and were taken to the hospital as a precaution, a spokeswoman for the airline said. She did not say how many people were injured.
Video and photographs from the scene showed Flight 2276, a Boeing Co 777 bound for Gatwick, engulfed in flames and thick black smoke at McCarran International Airport
Passengers were evacuated from the twin-engine, wide-body jet to the runway using emergency slides, officials said.
"Our crew evacuated the aircraft safely and the fire was quickly extinguished by the emergency services at the airport," the British Airways spokeswoman said..
According to preliminary information, the plane's left engine burst into flames on takeoff, said Ian Gregor, a spokesman for the Federal Aviation Administration's Pacific Division.
He said the plane was carrying 159 passengers and a crew of 13.
British Airways said the plane suffered a technical difficulty.
A photograph posted by the airport of the immediate aftermath of the fire showed the plane idled on the runway with its fuselage charred.
The fire temporarily delayed flights across the western United States.
Jacob Steinberg, a sports journalist for Britain's Guardian newspaper, wrote on Twitter that he had fallen asleep on the plane during takeoff and felt the jetliner come to "crashing halt.
Video of the aftermath here pic.twitter.com/3Uxnmz0ltr— Jacob Steinberg (@JacobSteinberg) September 9, 2015
"Could smell and see smoke but was on other side of plane. One person said fire melted a couple of windows," Steinberg wrote. "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."
A spokeswoman for British Airways, which is owned by IAG , said safety was always the top priority and the airline was providing passengers with hotel accommodation and other needs.