It added it first received the reports at about 5:05 p.m. Tuesday.
"As a precautionary measure, Heathrow Airport has stopped departures and officers based at Heathrow are now investigating the reports with colleagues from Heathrow Airport", she added.
A Heathrow spokesman said airport staff were continuing to monitor the situation.
It comes just weeks after a drone crippled Gatwick airport and grounded more than 1,000 flights.
Flights appeared to be taking off again about half an hour after Heathrow issued the statement, according to the Flightradar24 website.More news: Near-capacity toilets force Joshua Tree campgrounds to close amid government shutdown
"We are responding to a drone sighting at Heathrow", the airport said. Drones were reportedly spotted at the airport 67 times and authorities detained and released two suspects following investigations.
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.
Transport Secretary Chris Grayling said "the military are preparing to deploy the equipment used at Gatwick at Heathrow quickly should it prove necessary".
Heathrow and Gatwick recently also spent millions of pounds on military-grade anti-drone equipment.
Today, the British government announced a package of measures created to give police extra powers to combat drones. When a drone collided with a passenger plane over Quebec City, Quebec, last year, the plane landed safely.
Locals now get half a day's respite from noise when take-offs and landings switch to the opposite runway at 3pm, but Hacan claims this would be reduced to one third of a day.