The pursuit in the King Cross area began at around 6.15pm when a blue Volkswagen Scirocco ignored a police request to stop.
The Scirocco then travelled along Manor Drive, failing to give way at the junction with Free School Lane.
It continued before colliding with a tree, hitting the woman at the same time.
A police spokesman said: "The driver, a 51-year-old man, fled the vehicle but was detained by officers before being taken to hospital for treatment for his injuries. He has since been discharged.
"The pedestrian, a woman in her 60s, sustained minor injuries."
Anyone who saw the Scirocco before the incident or who has information is asked to contact PC 3387 Mark Maiden at the Western Safer Roads and Neighbourhood Support Team via 101, quoting 13170364927.
Information can also be passed to the independent crime fighting charity Crimestoppers anonymously on 0800 555 111.