It said it is working with police to prevent any threat to operational safety and apologised to passengers "for any inconvenience this may cause".
One user, called Nadim Baig, said: 'My luck, drone sighting and now my flight is at a standstill just before departure'.
Passengers are taking to social media to report that they are stuck on the tarmac at Heathrow this evening because of the incident.
York said he is "absolutely certain that there was a drone flying throughout the period that the airport was closed".
BBC producer Kathy Long, speaking from a plane waiting to depart at Heathrow, said passengers had not been told officially what was behind the delay.
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The UK's transport secretary Chris Grayling said on Twitter that the military was "preparing to deploy the equipment used a Gatwick" if necessary.
Whoever had their fun with a drone at Gatwick is about to hand loads more anti-drone powers to the police, as the Home Office has announced the results of a consultation into What To Do About Drones.
Heathrow and Gatwick responded by ordering military-grade anti-drone defenses worth "several million pounds".
The exclusion zone around airports is now one kilometre (half a mile) and this will be extended to five kilometres. Plane not going anywhere due to drones'.
From November 30 this year, operators of drones weighing between 250g and 20kg will also have to register and take an online pilot competency test.
Fines of up to £100 could be given for offences such as failing to comply with a police officer when instructed to land a drone, or not showing their registration to operate a drone.