The diamond fetched 20.5 million Swiss francs, equivalent to approximately $26.6 million, including the buyer's premium and other fees.
Weighing 9.51 carats, the stone is named after the late American arts patron Rachel "Bunny" Mellon, having been part of her private collection for decades.
It was previously sold in 2014 for $32.6 million and is graded Fancy Vivid Blue and Internally Flawless by the Gemological Institute of America.
The sale was part of a two-day series of jewellery auctions in Geneva, with rival Sotheby's also set to auction a significant pink diamond.