Minnie Hamilton from Harlaw Road, Balerno, was walking in Bavelaw Road around 11.20am on Monday, December 10, when she was hit by a blue Citreon C8.
She was taken to Edinburgh Royal Infirmary for treatment, but her condition deteriorated and she passed away on Wednesday, December 12.
Police are now appealing for anyone who witnessed the incident to come forward with information.
Constable Graham McKenzie said: “We know Bavelaw Road would have been busy at the time this collision happened, and we are appealing for anyone who may have been in the area and have seen what happened to contact us.”
Anyone with any information should contact Lothian and Borders Police on 0131 311 3131, or the independent charity Crimestoppers in complete anonymity on 0800 555 111.