The fire is believed to have started on a roof terrace to the rear of Lazenby's restaurant with firefighters entering through the front door to gain access.
North Yorkshire Fire and Rescue Service said they received a call around 10.08am this morning to reports of a fire on York Place.
Crews remain at the scene with one fire engine, it is believed two were in attendance.
North Yorkshire Police have closed York Place and are asking drivers to avoid the area with tailbacks starting to form on Albemarle Crescent.
A police spokesperson said: "The closure is expected to be in place for some time so please avoid the area if at all possible."
Two park and ride bus services are currently stuck on York Place, the 64 service which goes to the A64 park and ride as well as the 165 service which goes to the A165 Filey Road park and ride.
Neither service had many passengers on board and the fire is expected to have little impact on bus services in the area.
A spokesperson for East Yorkshire Buses, which run services along York Place, said: "All services which normally serve this route will divert via Westborough. Stops on York Place will be missed."
Seven Coffee Shop & Eatery gave free drinks to emergency services at the scene.
Lazenby's restaurant recently acquired new owners in June.