Arrivals and departures were suspended after the incident at 16:30 BST, a spokesman for the airport said. No passengers were aboard at the time.
Fifty Dreamliners worldwide were grounded in January after malfunctions with the plane’s lithium-ion batteries.
Boeing later modified the jets with new batteries and flights resumed in April.
The Ethiopian Airlines Dreamliner in the Heathrow incident – named the Queen of Sheba – flew from Addis Ababa to Nairobi on the first commercial flight since the grounding.
Pictures of the Heathrow fire showed the Queen of Sheba close to a building and surrounded by fire vehicles. London Fire Brigade said its crews were standing by to assist Heathrow staff.
Fire-retardant foam appeared to have been sprayed at the airliner, but no damage was immediately apparent.
A Heathrow spokesman said: “Heathrow’s runways are now fully open following an earlier fire on board an Ethiopian Airlines aircraft which the airport’s emergency services attended.
“The aircraft was parked on a remote parking stand. There were no passengers on board and there are no reported injuries at this time.
“The aircraft was parked on a remote parking stand and there were no passengers on board. Arrivals and departures were temporarily suspended while airport fire crews attended to this incident.
“This is a standard procedure if fire crews are occupied with an incident.”
Heathrow reopened shortly before 18:00 BST but is advising passengers to check the status of their flights with the airlines.
Meanwhile, Gatwick airport said it was experiencing minor delays on departing flights as it assisted Heathrow with flights that were diverted.
The battery problems followed production difficulties for the Dreamliner, marketed as a quiet, fuel-efficient aircraft carrying between 201 and 290 passengers on medium-range routes.
It was due to enter passenger service in 2008 but it was not until October 2011 that the first commercial flight was operated by Japan’s All Nippon Airways.
The Dreamliner’s electrical system drives air conditioning and hydraulic functions that are run from compressed air on traditional aircrafts.
British Airways is due to take delivery of the first two of its 24 Dreamliners, and Virgin Atlantic is to get the first of its 16 planes in September 2014.
Boeing shares fell more than 6% on the New York Stock Exchange on news of the fire.
A Boeing spokesman said: “We’re aware of the event. We have Boeing personnel on the ground at Heathrow and are working to fully understand and address this.”
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