All 172 passengers and six crew members evacuated and six passengers were later taken to hospital for further evaluation.
Footage showed passengers standing on the plane’s wing as ladders and slides were used to help them disembark safely.
Ground staff were also seen rushing to the tarmac to extinguish the blaze.
“We thank our crew members, [Denver] team and first responders for their quick and decisive action with the safety of everyone on board and on the ground as the priority,” the airline said in a statement.
Denver International Airport said no one was injured.
“Passengers were evacuated and the slides were deployed,” the airport said.
The FAA said it would investigate the incident. Boeing declined to comment, referring queries to American Airlines and investigators.
The plane, which is 13 years old according to flight tracking website FlightRadar24, was equipped with two CFM56 engines manufactured by CFM International, a joint venture between GE and Safran.
The engine fire follows a spate of aviation accidents this year, including the American Airlines jet that crashed with a Black Hawk helicopter near Washington DC, killing 67 people on board both aircraft in the deadliest plane crash in the US since 2001.
Meanwhile in Philadelphia, just days after that deadly crash, seven people died after a medical jet plunged to the ground and burst into flames.
