The incident happened in Oxford Street shortly after 2.30am today (January 28).
Officers attended and found a woman, who had been travelling in the car, with a leg injury.
She was taken to hospital for treatment where her condition was assessed as non-life threatening.
The driver of the car, a man, was arrested on suspicion of drink driving offences.
A spokesperson for Metropolitan Police said: “Police were called shortly after 02:30hrs on Sunday, 28 January, to a car in collision with a bus stop on Oxford Street near the junction with Rathbone Place.
“One woman who had been travelling in the car remains in hospital having sustained leg injuries. Her condition is not life-threatening.
“The male driver of the car has been arrested on suspicion of drink drive offences.”