A marked police car was following a blue Citroen C3 after it was spotted with a smashed windscreen in the Athersley North area on Sunday afternoon.
The car was on Fish Dam Lane, travelling in the direction of Royston, when it crashed with a white Range Rover Evoque travelling the opposite way.
The driver of the Evoque, a 32-year-old man, and the front seat passenger, a 32-year-old woman, both suffered minor injuries.
The five-year-old girl, who was travelling in the back of the Evoque, suffered serious injuries and was taken to hospital, where she remains.
The driver of the Citroen, a 29-year-old man, was also seriously injured and taken to hospital.
He has been arrested on suspicion of burglary and causing serious injuries by dangerous driving.
The Citroen was later identified as having been stolen during a burglary in Barnsley.
South Yorkshire Police have referred the incident to the Independent Office for Police Conduct (IOPC).
Police are appealing for anyone who saw the crash or motorists with dash-cam footage to call police on 101, quoting incident number 419 of February 28.