The Airbus A320, with 132 passengers and five crew on board from Geneva was hit as it approached Heathrow airport at about 12:50 PM local time yesterday.
After landing, the pilot reported an object - believed to be a drone that struck the front of the plane.
The Metropolitan Police's aviation security unit based at Heathrow which is leading the investigation said no arrests has been made so far in the case.
If confirmed, it's thought it would be the first such incident in the UK, the BBC reported.
A Civil Aviation Authority spokesman said it was "totally unacceptable" to fly drones - which are generally used to capture aerial film or photographs - close to airports.
Flying drones near airports is a punishable offence which could attract up to five years in prison in the UK.
