It weighs 7.03 carats, is smaller than a penny piece, and is one of only a handful of blue diamonds in existence.
The anonymous phone bidder has yet to name the gem, mounted on a platinum ring, auctioneers Sotheby's said.
The diamond was found in Cullinan mine in South Africa last year, and its clarity was graded as flawless - the highest designation.

Auctioneer David Bennett said: "It is a new world record price for a blue diamond."

It had a pre-sale catalogue estimate of 6.8 million to 10 million francs, excluding commission.
The hammer price excluding commission was 9.3 million francs.

The scarcity of the gems is in part down to the fact so few places in the world mine for blue diamonds.

Mr Bennett said: "For people who are looking to buy something that nobody else has, or somebody who wants something that is beyond beautiful, a blue diamond is going to be very difficult to find, so when they appear on the market, you have to have a go."
The stones get their colour when the chemical boron is present during formation.

In May 2008 a 3.73 carat diamond was sold by Sotheby's at auction for nearly $5m (£3.4m) setting the world record price per carat for any gemstone at auction.