The building was previously part of the Debenhams department store, which closed in May 2021 following another fire the previous month.
River Island and Levi’s had stores on the building’s ground floor, but both stores closed.
Before becoming a department store, it was part of the Palace Hotel, later to become the Liberal Club, designed by the architect John Lessels.
Former owners Legal and General submitted plans for a £50 million redevelopment which would have included a 207-room hotel, but the project never happened.
The site was later purchased by Criterion Capital, a real estate firm led by billionaire Asif Aziz.
He planned to turn it into the Zedwell Hotel, which if successful would be the first in Scotland.
A spokesperson for Criterion Capital said the company is “liaising with emergency services and relevant authorities to provide them with the support they need.”
In March the firm submitted a planning application to cover the building with a false façade, including an advertising screen.
A spokesman for the conservation body Edinburgh World Heritage said: “Fire is one of the greatest threats to our historic buildings and cultural heritage.
“It is necessary to stabilize and preserve as much of the structure of this listed building as possible.
“No action should be taken until an urgent investigation has been carried out to determine why the fire occurred.”