The hospital treating the pregnant Duchess of Cambridge said it "deeply regrets" giving out information about her condition to hoax callers from an Australian radio station.
Presenters posing as the Queen and Prince Charles got details from a nurse at King Edward VII hospital in London.
The hospital said confidentiality was taken seriously and telephone protocols are under review.
Prince William is currently visiting his wife at the hospital.
The Duke of Cambridge spent several hours visiting her on Monday and was there again during the day on Tuesday.
A spokesman for William and Catherine said he would be making no comment on the call.
Two presenters on Sydney-based radio station 2Day FM are reported to have convinced staff they were the Royals and were connected to the duchess's private nurse in the early hours of Tuesday morning.
The pair were given an update on her condition.
A spokesman for the hospital said: "This call was transferred through to a ward and a short conversation was held with one of the nursing staff. King Edward VII's Hospital deeply regrets this incident."
John Lofthouse, chief executive at King Edward VII's Hospital, said: "This was a foolish prank call that we all deplore."
The duchess, who was admitted to the hospital on Monday, is thought to be less than 12 weeks pregnant.
It has been confirmed she is being treated for acute morning sickness, or hyperemesis gravidarum.
In a statement on Tuesday evening, a St James's Palace spokesman said: "The Duchess of Cambridge is continuing to feel better. She and the Duke are immensely grateful for the good wishes they have received. She will remain in hospital at present."
Prime Minister David Cameron began his weekly Prime Minister's Questons by congratulating the Royal couple on the news that they are expecting a baby.
The announcement of the pregnancy came as all Commonwealth realms agreed to press ahead with a bill ending discrimination against women in the succession to the British throne.
It means William and Catherine's first child will become monarch, whether a boy or a girl.
Deputy Prime Minister Nick Clegg said the government would introduce the Succession to the Crown Bill in the House of Commons as soon as possible.
The legislation was agreed in principle at the Commonwealth heads of government meeting in Perth, Australia in October 2011.
Since then, the government of New Zealand has been gathering formal letters of consent from the 15 realms of the Commonwealth, that have the Queen as their head of state.
The succession bill will require amendments to some of Britain's key constitutional documents, including the Bill of Rights and Coronation Oath Act of 1688, the 1701 Act of Settlement and the 1706 Act of Union with Scotland.