The group is protesting against climate change.
A spokeswoman for BAA said the protestors were arrested at around 11am and were being held at the Heathrow police station.
Flights to and from Terminal One appeared largely unaffected and the whole incident seemed to have passed off without travellers being made aware of the disruption.
The four protestors managed to climb onto the plane and cover the tailfin with a banner that read 'Climate Emergency - No 3rd Runway'.
The plane had recently landed at Heathrow from Manchester.
The Greenpeace volunteers, two women and two men, waited until all the passengers had disembarked from the plane before they began their protest.
The demonstrators crossed an area of tarmac and climbed stairs onto the fuselage of the British Airways plane.
The protest comes two days before the end of a British government consultation into Heathrow expansion.
Greenpeace is calling for an end to all airport expansion and a cap on flights at present levels.
