The 85-year-old was killed in a collision near Asda, at the junction ofÂ Herten Way and Gliwice Way just before 2pm yesterday.
She was in a red Nissan Micra involved in a collision with a police van.
She was taken to hospital with serious injuries but has since died.
Three police officersÂ sustainedÂ minor injuries.
South Yorkshire Police has referred the incident to the Independent Office for Police Conduct.
Witnesses should call SouthÂ Yorklshire Police on 101 and quoteÂ incident number 498 ofÂ December 9.