Four people were hospitalised for smoke inhalation and another was treated at the scene.
The blaze broke out in the Wing Chun Academy, a martial arts centre off Hindley Street, just after midday on Tuesday.
It forced the evacuation of nearby buildings, including the Hotel Grand Chancellor, as about 80 firefighters and 18 fire trucks battled to bring it under control.
Several roads were closed and people were urged to avoid the area as smoke billowed from the building.
The blaze took half the city's firefighters about two hours to contain and a Metropolitan Fire Service spokeswoman said it had caused significant damage.
"Crews are currently digging away in the roof up there so they can make sure the fire is thoroughly out," she said.
"There's still some concern that the front facade of the building may collapse."
A guest at the Hotel Grand Chancellor, Sydneysider Molly Cooper, said she was doing her make-up when the alarms went off.
"I smelled smoke through the whole building," she told AAP.
"I think I was the last person to leave. I didn't expect it to be such a huge thing until I came outside.
"There were crowds everywhere, fireman everywhere, photographers."
Adelaide fire view from Leigh Street before shut to public #adelaidefire pic.twitter.com/X8JdAAdQE0 — David Maegraith (@DavidMaegraith) September 1, 2015
The owner of a nearby skate store, Allan Mawer, said the fire was "full on".
"All of a sudden they were pulling everyone back," he told AAP as the fire raged.
"That guy on the cherry picker's been up there for a good 20 minutes absolutely blasting the whole building (with water)."
Fire crews using cranes to contain building fire from above #adelaidefire @7NewsAdelaide @Y7News pic.twitter.com/HIPMG7JpJk — Stacey Lee (@Staceylee_) September 1, 2015
MFS assistant chief officer Roy Thompson said no one was inside the building when the fire started.
"Our main concern was the building collapsing," he said.
"That facade on the front of the Win Chung Academy was a major concern - bits and pieces actually started to fall off in the laneway."
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