The incident took place at around 1.30pm on June 4 outside B&M Bargains at Culverhouse Cross in Cardiff.
A 70-year-old woman was injured in the collision, which involved an orange Renault.
A 36-year-old woman has been arrested on suspicion of driving while under the influence of drugs.
A spokesperson for South Wales Police said: “A collision in the car park outside B&M Bargains at Culverhouse Cross continues to be investigated.
“We believe there were witnesses to the incident who left prior to our arrival.”
Officers are appealing for anyone who witnessed the collision or has dashcam, CCTV or mobile phone footage to contact South Wales Police quoting reference number 2600175041.
Information can also be provided anonymously through Crimestoppers.
Enquiries are ongoing.
