The man, who is in his 50s, was a front-seat passenger in a black Peugeot which police attempted to pull over in the Brierley area of Barnsley on Sunday.
The car was pursued by officers towards Park Road at around 5.55pm.
At the junction of Park Road and Brierley Road, the Peugeot was involved in a crash with a second car, a silver Road.
Three occupants of the Peugeot, including the driver, fled the scene on foot, leaving the front-seat passenger, who was seriously injured.
The four occupants of the Ford suffered minor injuries.
Anyone with information is urged to call police on 101 quoting incident number 691 of May 2.