The teenager was hit by the car while it was on routine patrol in Glasgow's Castlemilk area, on Saturday night.
She was taken to Yorkhill Hospital for treatment to her wrist, arm and cuts to her eye and was detained overnight.
The incident occurred at 8.45pm on Ardencraig Road, Castlemilk.
A spokesman for Strathclyde Police said: "At 8.45pm a 13-year-old girl was injured after being struck by a police car on routine patrol in Ardencraig Road, Castlemilk."
The circumstances of the incident are being investigated.