The incident happened on Queensferry Road around 9.35pm. it was incorrectly reported earlier that the collision had happened at 11.30pm.
The 33-year-old pedestrian, an Italian national who was on a break in the Capital, suffered two broken ribs and a punctured lung after being struck by the grey Toyota people carrier between Clermiston and Drumbrae.
She remains in a stable condition in hospital, and it is hoped that she will be able to make a full recovery and return to her home in southern Italy next week.
Police are renewing their appeal for witnesses to the incident, and are especially keen to trace the driver of a dark silver coupe, similar to a Toyota Celica or MR2, which was seen travelling northbound on Queensferry Road at the time of the incident.
A Lothian and Borders Police spokesman said: “We believe that the driver of this car may hold information that can assist our inquiries, and we would urge them to contact police as soon as possible.
“Similarly, anyone else who witnessed the incident should also get in touch.”