Emergency services were called to the scene but no injuries were reported.
The spokeswoman said: “Emergency services are attending an incident involving two aircraft on the airfield.
“No injuries have been reported but emergency services are attending to ensure all passengers and crew are safe and well.”
The nature of the incident was not clear at first, with witnesses initially reporting the wings of two planes hit into each other.
But journalist Dan Sabbagh said he was on a Korean Air plane whose wing clipped the tail of an Icelandair plane.
I'm on Korean Air plane that clipped an Icelandair plane at Heathrow - a passenger on the other side saw the incident told me the wing of our plane damaged the others' tail.
Pic from earlier of the police and fire on the ground credit: Noah Sabbagh pic.twitter.com/2JcJBB09F4
— Dan Sabbagh (@dansabbagh) September 28, 2022
Passengers sat on planes on the tarmac reported seeing police cars and fire engines on the runway after an incident.
One passenger who claimed to have been on a flight said they were taxiing on the runway when they “suddenly got stopped by all these emergency services”. They said passengers were then told they were returning to the gate “due to a technical issue”.
A London Ambulance spokesman said: “We were called today at 8.06pm to reports of an incident at Heathrow airport.
“We sent a number of resources to the scene including members of our Hazardous Area Response Team (HART), a clinical team leader, a cycle responder and an incident response officer.
“We attended a reception centre for passengers but nobody required treatment or needed to be taken to hospital.”
The incident is being investigated.