The airport confirmed in a statement issued at around 5.45pm aircraft were not currently leaving the airport.
The statement read: "We are responding to a drone sighting at Heathrow and are working closely with the Met Police to prevent any threat to operational safety.
"As a precautionary measure, we have stopped departures while we investigate. We apologise to passengers for any inconvenience this may cause."
A Met Police statement added: "At approx 5.05pm today we received reports of a sighting of a #drone in the vicinity of Heathrow airport.
"As a precautionary measure, @HeathrowAirport has stopped departures and officers based at Heathrow are currently investigating the reports with colleagues from airport."
It comes just weeks after Gatwick airport was forced to suspend flights for more than 36 hours following reports of drone activity over the airfield.
The government on Monday (January 7) announced new powers for police to combat illegal drone activity in the wake of the Gatwick farrago, as well as the extension of drone exclusion zones around airports.
Transport secretary Chris Grayling said the military was on standby to intervene at Heathrow, if necessary, as it did during the Gatwick drone disruption.
“We are in contact with Heathrow airport concerning the drone sighting," said Grayling.
"I have already spoken to both the home secretary and defence secretary and the military are preparing to deploy the equipment used at Gatwick at Heathrow quickly should it prove necessary.”
A Heathrow spokesperson confirmed at around 6.30pm departures had resumed.
“We continue to work closely with the Met Police to respond to reports of drones at Heathrow," they said.
"Based on standard operating procedures, working with Air Traffic Control and the Met Police, we have resumed departures out of Heathrow following a short suspension.
"We continue to monitor this situation and apologise to any passengers that were affected by this disruption."
Derek Jones, chief executive of Kuoni parent Der Touristik UK, took to Twitter to reassure clients flying from Heathrow the operator was on hand to assist.
"We’re already on the case contacting #Kuoni customers travelling out of #Heathrow this evening," said Jones.
"[We] will do everything we can to take care of them and make alternative plans if necessary."