The BA flight from Geneva with 132 passengers and five crew onboard was hit as it approached the London terminal at 12:50 on Sunday.
After safely landing the aircraft, the pilot reported that an object, which he believed to have been a drone, collided with the front of the Airbus A320.
If confirmed, the incident is thought to be the first of its kind to happen in the UK, reports BBC News.
BA said it would give the police "every assistance with their investigation" with authorities confirming that no arrests have been made.
A Metropolitan Police aviation security unit based at Heathrow is due to lead the investigation into the occurrence.
A BA spokesperson said: "Our aircraft landed safely, was fully examined by our engineers and it was cleared to operate its next flight."
Following the episode, a spokesperson for the CAA said it was "totally unacceptable" to fly drones, which are commonly used to capture aerial film or photographs near to airports.
Furthermore, Steve Landells, of the British Airline Pilots Association (Balpa), said it had been "only a matter of time before we had a drone strike".
He also called for greater enforcement of existing rules.