It hopes the move will encourage passengers to bring their own reusable containers and bottles and says it will deploy cup collection points around its terminals in the next month.
London’s biggest airport also plans to eliminate other sources of single-use plastics such as bottles and straws from its buildings.
The airport estimates only 0.25% of plastic cups are currently recycled, meaning only 33,750 of the 13.5 million used at Heathrow each year are disposed of properly.
CEO John Holland-Kaye said: “As a small city, we are committed to reducing our impact on the environment and using all our influence to ensure individual companies working within our boundaries do so as well.
“This announcement takes us one step further, ensuring all single-use coffee cups at the airport are able to be recycled with additional support from Heathrow.”