The Scottish Fire and Rescue Service (SFRS) was called to a blaze affecting several properties at George IV Bridge at 6:18 a.m. on Tuesday.
One person was taken to hospital and another was treated at the scene.
Images from the area on Tuesday morning showed smoke pouring from a branch of Patisserie Valerie, next door to the Elephant House cafe, which was made famous as the place where JK Rowling wrote much of her early Harry Potter series.
SFRS said four fire engines and a height appliance remained at the scene at 7 a.m. on Wednesday morning.
Some road closures were still in place.
*** ROAD CLOSED *** – Due to a fire #GeorgeIVBridge and #CandlemakerRow will remain closed for the foreseeable. Please avoid the area meantime. Emergency services remain in attendance. #Planahead #Edinburgh #RoadClosure
— EdinburghPolice (@EdinburghPolice) August 25, 2021
Elephant House owner David Taylor told the BBC his building had suffered smoke and water damage, although 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.
“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 percent of our festival trade.”
Police in Edinburgh wrote on Twitter: “Due to a fire #GeorgeIVBridge and #CandlemakerRow will remain closed for the foreseeable.
“Please avoid the area meantime. Emergency services remain in attendance.”
By Lucinda Cameron