Two telephone bidders battled for the prized jewel before some 150 people attending the auction held at a luxurious hotel in Geneva.
"It's a new world record... It's the highest price ever paid for a fancy vivid pink diamond," said auctioneer David Bennett.
He added only that the buyer was a private individual from Asia.
Sotheby's had valued the "exceptional" pear-shaped diamond, mounted on a ring, at between $28-38 million.
It was discovered less than five years ago in a South African mine. The seller was the New York-based company Cora International.
The stone with the name "Unique Pink" was certified a fancy vivid pink diamond, the most sought after colour in pink diamonds, by the Gemmological Institute of America.
The sale beats the previous record for a fancy pink diamond, set last November, when a 16.08 carat diamond sold for $28.5 million, also at Sotheby's in Geneva.
Also on Tuesday Sotheby's sold a blue diamond, weighing 7.32 carats, for $17.1 million.
On Wednesday the magnificent spring jewel auctions continue in Geneva with what Christie's says is the biggest ever vivid blue diamond to go on the auction block.
The 14.62-carat blue diamond, known as the "Oppenheimer Blue", is estimated at between $38-45 million.
The jewel belonged to Britain's Sir Philip Oppenheimer (1911-1995), a kingpin in the world diamond market for nearly 50 years at De Beers.