The auction house said "The Historic Pink Diamond" only recently resurfaced after sitting in a bank vault since the 1940s. A buyer was not disclosed by Sotheby's.
The vibrant cushion-cut diamond is considered extremely rare. It was sold as part of the auction house's Magnificent Jewels and Noble Jewels sale.
The princess was the niece of Napoleon I and a relative of King George II and the tsar of Russia. She amassed a collection of pearls, diamonds and other jewelry considered second only to the collection of Empress Eugenie, the wife of Napoleon III, Sotheby's said.
Mathilde died in 1904. The pink diamond was believed among her jewels auctioned in Paris in June 1904 and later acquired by William Andrews Clark Sr., a U.S. senator, industrialist and entrepreneur who died in 1925.
After his death, the stone passed to a daughter, Hugette Marcelle Clark, who died in 2011.
The diamond is also considered prized for its cut, a classic, non-modified version of the cushion, Sotheby's said.
The auction house considers the market for colored diamonds and other precious gemstones strong and pink diamonds among the rarest. In October, Sotheby's sold another pink diamond for $17.8 million.