The blaze was reported to the fire services at 6:18am on Tuesday morning, with appliances on the scene within minutes.
Images shared on social media show smoke billowing from buildings on both George IV Bridge and Candlemaker Row.
Emergency services have warned the public to avoid George IV Bridge, Candlemaker Row and neighbouring streets as they tackle the blaze.
At least one person has been taken to the Royal Infirmary of Edinburgh.
The extent of the damage caused by the fire remains unclear.
A number of businesses in the vicinity will be closed until further notice and bus services have been diverted.
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1. George IV Bridge fire
Height appliances are being used to tackle the blaze. Photo: Copyright Matt Donlan
2. George IV Bridge fire
Pictures show how the fire has spread to Candlemaker Row. Photo: Copyright Matt Donlan
3. George IV Bridge fire
Greyfriars Bobby amid the chaos. Photo: Copyright Matt Donlan
4. George IV Bridge fire
The area has been cordoned off while emergency services tackle the fire. Photo: Copyright Matt Donlan