The 72-year-old woman was crossing the road outside at the junction with The Pleasance at around 10:40 pm when she was involved in a collision with a Mercedes B Class car.
Police said the vehicle stopped and remained at the scene, however it was still surrounded by a cordon several hours after the incident, with traffic being diverted around the area.
Sergeant John Easton from the Road Policing Unit in Edinburgh said: “At this time we are working to establish exactly what has happened during this incident and we would urge motorists or members of the public who were in the area at the time and witnessed the collision to come forward.
“The Pleasance area would have been quite busy due to ongoing Festival events and so anyone with information is urged to contact police immediately.
“In addition, vehicles with dash-cam footage, which may be able to assist with this inquiry should also get in touch.”
Those with information can contact the Road Policing Unit in Edinburgh via 101 and quote incident number 4371 of the 7th August.
A spokesperson for the Scottish Ambulance Service said: “We received a call at 2234 hours on Tuesday 7 August to attend an incident on the Cowgate in Edinburgh.
“We dispatched one ambulance to the scene and one male patient was taken to the Edinburgh Royal Infirmary.”