The 77-year-old was walking in Seedhill Road, near its junction with Lacy Street in Paisley, when she was struck by what has been described as a "dark or black medium-sized car".
The car failed to stop and was driven along Seedhill Road towards Mill Street.
The injured woman was taken by ambulance to the town's Royal Alexandra Hospital where she was treated for a head injury. She has since been released from hospital.
The incident, which police are describing as a hit-and-run, happened around 5pm on Friday.
Constable Kevin Craig, of Renfrew police office said: "This was a terrifying ordeal for the woman, and one which has left her badly shaken.
"Extensive inquiries are ongoing to trace the car involved in this incident and to establish who was driving this car at the time.
"The car involved must have sustained some damage, probably to the front passenger side, and possibly the windscreen, so I would ask that anyone who has seen a car that matches the description to get in touch."
He said Seedhill Road would have been busy around the time of the incident on Friday night, and wants any witnesses to the incident, or anyone who may have information to come forward.
Anyone with information on this incident should contact Renfrew police office on 0141 532 6100, or call 101, the new non-emergency number for police. Alternatively calls can be made to Crimestoppers on 0800 555 111, where anonymity can be maintained.