One of those flights suspended is a flight to Belfast.
The airport said the decision has been taken as a precautionary measure.
It said it is working with police to prevent any threat to operational safety.
Arriving planes are continuing to land at Heathrow.
The airport is Europe’s busiest hub in terms of passenger numbers.
Heathrow Airport said in a statement this evening: “We are responding to a drone sighting at Heathrow and are working closely with the Metropolitan 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.”