The incident happened at around 8.30 pm on Friday at the car park outside the Magnet Bar on Culmore Road.
An officer, posting on the PSNI’s Foyle Facebook page, said: “At around 8:30 pm on Friday night this blue people carrier, with a roof rack and bearing R plates, parked at the Magnet Bar.
“The female driver stayed in the car whilst two females went into the shop. When they arrived back to the car the driver reversed out the parking space but scraped a 1 week old, brand new black VW Golf GTI all up the side.
“We know the driver was aware as she panicked and stalled the car 4 times.
“She seemed young and inexperienced. One of the passengers then had to take over and reverse the car out.
“The original driver then got back in and drove off.
“Car lovers will be especially horrified but I’m sure like me the rest of us are just angry at the lack of respect, morals and decency this driver has shown.
“If this is you it is time to call us and own up.”
Police said officers are checking CCTV of the incident to try to identify the driver and that the passengers in the car can be compelled to inform the PSNI of who was driving or face prosecution.