The Scottish Fire and Rescue Service was called at 7.20pm to a report of a burning smell coming from a house above Starbucks, and smoke is also coming from the property.
Six fire engines and a higher reach appliance have been dispatched to the scene and are conducting an investigation as to the cause of the smell, which is believed to be electrical.
There are also reports of smoke coming from the property.
The occupants of the premises have been evacuated while fire crews are searching for the cause.
A Police Scotland spokesman said: "Police in Edinburgh are currently supporting the Scottish Fire and Rescue Service in George Street following a report of a fire. A road closure is currently in place and the public are urged to avoid the area if possible."