Teams from Scarborough Filey and Robin Hood's Bay were deployed to the fire on the flat roof of the store in front of a first floor flat on Aberdeen Walk at 2.24pm.
The road had to be shut to allow an aerial ladder platform to be set up.
A wooden beam and a small amount of roofing felt were damaged.
North Yorkshire Fire and Rescue Service said: "The cause is believed to be careless use of a blow torch.