Some 140 firefighters needed around six hours to bring the blaze under control after they rushed to the scene at 1:30 am local time (0500 IST Wednesday).
The mansion is considered one of the finest examples of mid-17th-century French architecture, featuring frescoes by Charles Le Brun and other masters of the day, and is part of a World Heritage site along the banks of the river Seine.
The fire, which broke out overnight on the roof of the building, "spread pretty fast because the building is empty and in the midst of renovation", fire service Lieutenant-Colonel Pascal Le Testu told AFP.
"Now we have to see how badly the structures were affected as well as the state of the artworks inside that may have been reached by smoke and flames, but also water, despite our utmost efforts to protect them," he added.
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Around a dozen neighbours were evacuated, while one firefighter was slightly injured.
Built in the 1640s at the eastern tip of the Ile Saint-Louis, the mansion was designed for a wealthy financier, Nicolas Lambert, by the architect Louis Vau, who went on to oversee an expansion of the Chateau de Versailles for Louis XIV.
The 2007 acquisition of the mansion by Prince Abdullah Bin Abdullah Al-Thani, brother of Qatar's emir, from the Rothschild banking family for some 60 million euros (USD 85 million) sparked a dispute as heritage activists feared he would destroy a cultural gem.
A French court initially blocked his plan to modernise the mansion, including installing a vehicle lift.
The dispute was finally resolved in January 2010 when the prince signed an agreement with the heritage association Historic Paris after weeks of delicate government-supervised negotiations.