No passengers were aboard when a fire started inside the plane as it was parked in a remote location at the airport, the BBC reported.
Arrivals and departures were suspended to allow fire fighters to deal with the blaze, a Heathrow spokesman said.
There were no reports of injuries.
Battery malfunctions forced the grounding of 50 Dreamliners in January. Boeing has modified the jets with new battery containment systems. There was no immediate word on what sparked Friday's fire.
None of the previous fires involved injuries or loss of life. Two of the fires, including the Heathrow fire and one in January at Boston's Logan Airport, occurred in jets that were on the ground being serviced.
The prior fires involved the lithium-ion batteries that are not in use in flight, but only while the jets are on the ground.
The first of the incidents, however, involved an All Nippon Airways 787 that was forced to make an emergency landing after a battery alarm signal was activated.
The incident occurred January 15. At the time CNN reported that people in the plane that was carrying 129 passengers at the time, noticed a burning smell in the plane.
The National Transportation Safety Board said in an online posting it was "sending accredited representative to London-Heathrow to assist in investigation of fire aboard Ethiopian Airlines B-787," The Wall Street Journal reported.
A British team from the U.K. Air Accident Investigation Branch is also looking into the fire, the Journal said.
In a statement, Boeing said, "We're aware of the 787 event @Heathrow Airport and have Boeing personnel there. We're working to fully understand and address this."
On the New York Stock Exchange, Boeing stock closed down close to 5 percent on the day, leading the blue-chip Dow Jones industrial average in declines.
The DJIA closed flat, gaining 0.02 percent on the day. gaining 3.38 points to 15,464.30.
2014: The Year in Music [PHOTOS]