The incident happened while the aircraft was parked on tarmac at the west London airport.
An airline spokesman said: “A freighter aircraft has been damaged while stationary on stand.
“As a freighter-only aircraft there were no passengers on board.
“Safety is always our highest priority and we are investigating the matter.”
Images posted on social media show the aircraft, believed to be a Boeing 787, surrounded by more than a dozen emergency services vehicles, including police, fire brigade vehicles and ambulances.
The incident is not affecting other flights at Heathrow.