Officers on patrol spotted the vehicle in Whitehorse Road at around 5.50am today (March 28).
Police say they tried to stop the vehicle, but it failed to do so.
It then crashed into another car at the junction of Devonshire Road and Whitehorse Road.
The driver of the allegedly stolen vehicle, a 38-year-old man, was found injured and taken to hospital.
His condition was later assessed as not life-threatening or life-changing.
He has now been arrested on suspicion of theft of a motor vehicle and other driving offences.
He remains in police custody.
The driver of the other car did not require medical treatment.
A spokesperson for Metropolitan Police said: “At around 5.50am on Friday, 28 March officers on patrol spotted a stolen vehicle in Whitehorse Road, Croydon.
“Officers attempted to stop the vehicle but it failed to do so.
“The vehicle then collided with another vehicle at the junction of Devonshire Road and Whitehorse Road.
“Officers attended alongside the London Ambulance Service and the London Fire Brigade, and the driver of the stolen vehicle, a 38-year-old man, was taken to hospital.
“His condition has been assessed as not life-threatening or life-changing.
“He has been arrested on suspicion of theft of a motor vehicle and other driving offences.
“He remains in custody.
“The driver of the other car did not require medical treatment.”