British police said the fire is being treated as unexplained.
The entire fleet of 787s was grounded in January for problems involving the plane's lithium-ion batteries. One caught fire at Boston's Logan airport.
The planes resumed flying in May after Boeing made redesigns to the battery system that were approved by global aviation regulators. Ethiopian was the first airline to resume using the 787.
Boeing shares fell $7.20, or 6.7 percent, to $99.68, around midday in New York.
Boeing spokesman Marc Birtel said in an email to The Associated Press that the company has personnel at looking into the event at Heathrow.
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