The pedestrian was involved in a collision with a a silver Honda Jazz near the entrance to Sainsbury's in Reading Road on Friday May 9.
The incident took place at about 4.10pm and the woman was air lifted to hospital with serious head and body injuries.
The road was closed for approximately two-and-a-half hours while emergency services worked at the scene, and officers investigated the circumstances of the collision and recovered the vehicle involved.
PC Melonie Powell, from the Road Death Investigation Team, said: “The pedestrian died last night in hospital following this collision and our thoughts are with her family.
“We are continuing to investigate the circumstances and all parties involved have been assisting with enquiries.
“I would like to continue to appeal to anyone who witnessed the collision who hasn’t already spoken to police to get in touch.”
If you witnessed the collision call the Thames Valley Police 24-hour Enquiry Centre on 101, quoting URN 1055 of 09/05/14.