At around 12.30am in the early hours of Friday 28 September 2012, North Yorkshire Fire and Rescue service were called to the fire which was started in a wheelie bin positioned outside the loading bay doors on Union Street.
Damage was caused to the loading bay doors as well as smoke damage to the interior of the shop.
Police are appealing for anyone who was in the area on Thursday night or Friday morning and saw anything suspicious to contact them.
Please call North Yorkshire Police on 101, select option 2 and ask for Detective Constable Claire Brown at Harrogate CID.
Alternatively, you can pass information anonymously to Crimestoppers on 0800 555 111, quoting reference 12120162718.