Two drivers were involved in the crash on the taxiway just after 06:00 GMT.
At least 20 British Airways flights have been delayed by the incident, although the airfield remains open.
Passengers on one plane had to disembark after the crash, a Heathrow spokeswoman said.
Hi, we are dealing with a serious accident involving two vehicles on the airfield. The airfield remains open and we will work to minimise disruption to our passengers’ journeys. Thank you.
— Heathrow Airport (@HeathrowAirport) 14 februari 2018