Scotland Yard said a “full criminal investigation” had been launched into the incident, during which police officers were able to spot the drone for themselves.
The sighting meant that all departing flights were suspended causing delays for thousands of passengers.
The disruption followed repeated sightings of drones around Gatwick just before Christmas, which led to the airport shutting down for around 32 hours.
Heathrow airport, which is also working with the Met Police, said it was monitoring the situation and apologised to passengers affected by the disruption.
A Ministry of Defence spokesman said: “We are deploying specialist equipment to Heathrow Airport at the request of the Metropolitan Police.”
Met commander Stuart Cundy said: “We are carrying out extensive searches around the Heathrow area to identify any people who may be responsible for the operation of the drone,” he said.
“The illegal operation of drones at an airfield is extremely dangerous.
“It is an offence to endanger the safety of an aircraft; anyone found guilty of this offence could face a life sentence.
“We are deploying significant resources – both in terms of officers and equipment – to monitor the airspace around Heathrow and to quickly detect and disrupt any illegal drone activity; some of which are as a result of learning from the incidents at Gatwick.”