North Yorkshire Fire and Rescue Service confirmed that 'a number of crews' are at the scene of the fire on Stirling Road within the Clifton Moor retail park.
Footage from the scene shows smoke pouring from the restaurant building, which is adjacent to the large Tesco superstore and a KFC outlet.
Witness Sam Dixon-French, who is holidaying in the area from Sussex, said the outlet was 'well alight'.
Emergency services have not yet confirmed whether anyone has been injured.
It is the second major fire in the area following a blaze which destroyed the B&M Bargains store at Clifton Moor in October 2018. An investigation later found a discarded cigarette had ignited combustible material in a storage yard behind the premises and the flames had rapidly spread inside while the shop was trading. Customers were evacuated and nobody was injured.