Officers were called at 8.11am today (December 7) to a multi-storey car park at Terminal 3 following reports of multiple people being assaulted.
A group of men sprayed several individuals with what is believed to be a form of pepper spray before fleeing the scene, according to the police.
Armed response officers attended and arrested one man on suspicion of assault.
He remains in custody as the police continue their inquiry to track down further suspects.
The London Ambulance Service was present, and the victims were taken to hospital.
Their injuries are not deemed to be life-changing or life-threatening.
Commander Peter Stevens said: “At this stage, we believe the incident involved a group of people known to each other, with an argument escalating and resulting in a number of people being injured.
“Our officers responded quickly and there will be an increased police presence at Heathrow Airport throughout the morning, to continue enquiries and ensure the safety of those in the area.
“We are not treating this incident as terrorism. I understand the public’s concerns and would like to thank those in the area for their cooperation this morning.”
There is currently some disruption to traffic in the area.
Despite the incident, Terminal 3 remains open.
Anyone with information about the incident is asked to call the police on 101, quoting CAD 1803 7 DEC.

