North Yorkshire Police said the woman was hit by a silver Ford Mondeo in the car park of the town's Aldi store at 5.30pm on Saturday, December 15.
A spokesman today said: "The pedestrian was taken to Harrogate Hospital to receive treatment for a broken leg.
"We are requesting the public’s assistance to help establish the full circumstances surrounding the incident."
Anyone with information is asked to email [email protected] or call 101, select option 2, and ask for Sheree Evans.
Information can also be passed on anonymously via Crimestoppers on 0800 555 111.
Please quote the North Yorkshire Police reference number 12180232973.