The girl is understood to have been struck as her mother was parking in the car park behind Hounslow West tube station on Wednesday (August 13) morning.
Police officers and medics tried to resuscitate the youngster but she was later pronounced dead at St Mary's Hospital, in Paddington.
Police, ambulance crews and firefighters were called to the car park in Bath Road shortly before 9.40am.
DCI Iain Miller, of British Transport Police, said: "Our officers attended, alongside colleagues from the Metropolitan Police Service and London Ambulance Service, and discovered a child - a six-year-old girl - had sustained fatal injuries having been struck by a car being driven by her mother.
"It is clear that both mother and child arrived together in the car park and the accident occurred during a parking manoeuvre.
"Specialist officers are now providing full support to the girl's family whilst detectives are working to determine exactly how the incident occurred."
A spokesman for the London Ambulance Service said the girl had gone into cardiac arrest after the crash.
On Wednesday evening, a small patch of sand appeared to mark the spot where the girl had been hit.
One man living around the corner from the scene of the crash said he had heard a scream, which he assumed was that of the girl as she was hit, before sirens and the whirring blades of London's Air Ambulance filled the air.
But many of those in the neighbourhood remained oblivious to the tragedy which had unfurled almost on their doorstep.
* Anyone with information about the incident is asked to call British Transport Police on 0800 40 50 40.