The vehicle smashed through two boundary walls outside The Perfumed Garden in Chapel Allerton, shifting an entire section of the shop’s frontage by several inches and destroying newly-built wooden display stands.
The doorway to a flat above was cracked, one of the shop windows was smashed and gas pipes were also damaged.
A West Yorkshire Police spokesman said officers were sent to the shop in Harrogate Road after the crash was reported at 12.20am on Friday.
He said it was reported that a car had crashed into the shop but did not remain at the scene.
The car was described by witnesses as a blue Vauxhall Astra but the registration had not been recorded.
"The driver was male with short black hair, possibly Asian or eastern European," the spokesman said.
Anyone with information on the whereabouts of the vehicle or the identity of the driver is urged to call officers on 101, quoting log number 20 of Jan 12.