George IV Bridge and Candlemaker Row will stay closed after the fire which spread through the historic buildings on Tuesday morning.
The Scottish Fire and Rescue Service received a call around 6.18 am and well over 100 firefighters were on the scene throughout the day battling the blaze.
It is understood that the alarm was raised by a cleaner in the Elephant House Cafe, and the cafe, along with Patisserie Valerie and Oz Bar all suffered damage.
Elephant House owner David Taylor, told the BBC the building had suffered smoke and water damage, though the fire had not spread to it.
He told the broadcaster: “I feel absolutely gutted about this.
“At best, we can hope for opening in a few weeks’ time, but if there is structural damage too then it isn’t bearable to think about.”
He added: “It’s really quite disturbing because we had just got back to some semblance of normality after two years, although we were only running at about 50% of our festival trade.”
Flats above Patisserie Valerie were evacuated and Chambers Street was also closed off, although it will be open again today.
Emergency services will be remaining at the scene.
In a social media post, Police Scotland wrote: “Due to a fire George IV Bridge and Candlemaker Row will remain closed for the foreseeable.
“Please avoid the area meantime.”