The incident between a car and a pedestrian happened in Roman Way just after 1pm today (January 3).
Officers and London Ambulance Service crews attended and found a man injured.
He was taken to hospital for treatment where his condition is currently unknown.
No arrests have been made as police enquiries continue.
Bus routes 96, 428 and 492 are on diversion as the incident is being dealt with, according to AA.
A spokesperson for London Ambulance Service said: “We were called at 1.07pm today (3 January) to reports of a road traffic collision on Roman Way, Crayford.
“We sent an ambulance crew and a paramedic in a fast response car to the scene.
“We treated a man at the scene and took him to a major trauma centre.”
A spokesperson for Metropolitan Police said: “A car was in collision with a pedestrian in Stadium Way, Crayford at 13:07hrs on 3 January.
“A man was taken to hospital. We await an assessment of his condition.
“There has been no arrests.”
