The incident comes as unwelcome news for Chicago-based Boeing Co., whose Dreamliners were cleared to fly again in April after a four-month grounding amid concerns about overheating lithium-ion batteries.
Heathrow said there were no passengers aboard the Ethiopian Airlines plane, which was parked at a remote stand of the airport, and runways reopened after about an hour. British police said the fire is being treated as unexplained.
Boeing spokesman Marc Birtel said in an email that the company had personnel on the ground at Heathrow and "is working to fully understand and address" the situation.
Ethiopian Airlines was the first airline to resume using the 787, with a flight on April 27 from Ethiopia's capital of Addis Ababa to Nairobi, Kenya, after the battery incidents.
The airline could not immediately be reached for comment.
Television images showed nearly a dozen fire trucks on the scene at Heathrow and firefighters standing around the Ethiopian Airlines plane, which was parked on a remote stand.
Fire-retardant foam appeared to have been sprayed, and it was not immediately clear if there was damage to the plane.
The Dreamliner suffered battery incidents in January, including an emergency landing of one plane and a fire on another. U.S. federal authorities lifted the grounding order on April 19, and several airlines have recently resumed flying their Dreamliners.
None of the incidents caused any serious injuries. But the January grounding embarrassed Boeing and disrupted schedules at the eight airlines that were flying the planes. The company had delivered 50 of the planes worldwide.
Boeing never did figure out the root cause of the battery incidents. Instead, it redesigned the battery and its charger. The changes included more heat insulation between each cell and charging the battery to a lower maximum voltage.
Shares in Boeing fell 6.5 per cent to $99.58 on news of the Heathrow fire.