"As a precautionary measure, Heathrow Airport has stopped departures and officers based at Heathrow are now investigating the reports with colleagues from Heathrow Airport", they said.
It added it first received the reports at about 5:05 p.m. Tuesday. "They've only given us one update to say it was because of drone activity in departures".
"We are now responding to a drone sighting at Heathrow and are working closely with the Met Police to prevent any threat to operational safety", the airport's press office said in a statement.
Several passengers stuck at the airport - including those on board aircraft - have also tweeted to confirm that they have been told about the drone sighting.
Transport Minster Chris Grayling said the military are "preparing to deploy equipment used at Gatwick should it prove necessary". "We apologize to passengers for any inconvenience this may cause".
Planes could come in to land on both runways at the same time during busy periods, Heathrow has proposed, to help maximise its capacity ahead of expansion. More than 140,000 passengers had their flights disrupted and more than 1,000 flights were affected between December 19th and December 21st 2019.
Gatwick has since said it has invested in anti-drone technology, while Heathrow said that it would do so.
Meanwhile, UK government introduced new police powers against drones flown near airports this week.
Police could also fine drone users failing to comply with authorities or present registration to operate a drone up to £100.
The exclusion zone around airports will be extended to approximately a five kilometre radius, with additional extensions from the end of runways.
Ministers announced that from 30 November operators of drones weighing between 250g and 20kg will be required to register and take an online drone pilot competency test.