Police were called just after5pm.
An airport spokesman said they Heathrow is working with the Metropolitan Police and had stopped all flights as "a precaution".
ITV reporter Sarah Rogers confirmed the closure of the runway, writing on Twitter: “Grounded at #Heathrow whilst waiting to fly home to Manchester, first officer says flights suspended whilst police investigate possible #drone activity…”
Many passengers, some of which are trapped inside aircrafts, have taken to social media to vent their frustration.
One concern is this going to take 3 days like the Gatwick Drone in December last year.
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.— Heathrow Airport (@HeathrowAirport) January 8, 2019