The plane, flight BA727, was struck around 12.50pm Sunday after flying from Geneva, but managed to land safely at Heathrow Terminal 5.
There were no reported injuries.
A Met Police spokesman said they were investigating and no arrests had been made.
The spokesman said the pilot had told police he "believed a drone had struck the aircraft".
Aviation police said on Twitter that they were speaking to the pilot involved and added: "This is dangerous, it is also a crime. Please be aware of the rules before you start flying a drone."
A British Airways spokesperson said the plane was examined by engineers who said no major damage was done.
He said: "Our aircraft landed safely, was fully examined by our engineers and it was cleared to operate its next flight."