The cake, which was still in its original box, was sold online by an American auction house.
The box contains a card from the 1981 wedding, which reads: "With best wishes from Their Royal Highnesses, the Prince & Princess of Wales."
A spokesman from Nate D Sanders Auctions in Los Angeles said the buyer was a private collector.
Sam Heller said there was a dedicated group of royal cake collectors.
Some have bought cakes dating back to the days of Queen Victoria, who married in 1840, he said.
In April, a slice of cake from the Duke and Duchess of Cambridge's wedding sold at auction for £420.
A 33-year-old slice of cake from Prince Charles and Princess Diana's wedding has been sold for $1,375 (£828).