The King Edward VII hospital in London acknowledged that the Australian radio station made the hoax call to the hospital in the early hours on Tuesday - and that the hospital fell for it.
The 30-year-old Duchess of Cambridge is pregnant and is being treated at the hospital for severe morning sickness.
A woman using the often-mimicked voice of Britain's monarch asked after the duchess' health - and was told by a nurse that Kate "hasn't had any retching with me and she's been sleeping on and off."
"She's sleeping at the moment and she has had an uneventful night. She's been given some fluids. She's stable at the moment," the kindly nurse informed the supposed queen and prince on the station's recording. A dog yaps in the background while the alleged queen and prince talk about travelling to the hospital to check in on the patient.
"I would suggest that any time after 9 o'clock will be suitable to visit," the nurse said. "We'll be getting her freshened up."
The duchess is married to the queen's grandson, Prince William.
The hospital says the call had been transferred to the ward and the conversation was held with one of its nursing staff. Its telephone protocols are now being reviewed, the hospital said in a statement.
The Australian station 2DayFM placed the recording of the conversation on its website.
Australian radio personalities Mel Greig and Michael Christian later apologised for the hoax - along with their station.
"We were very surprised that our call was put through. We thought we'd be hung up on as soon as they heard our terrible accents," they said in a joint statement with the station. "We're very sorry if we've caused any issues and we're glad to hear that Kate is doing well."
The duchess is spending her third day in the hospital. William visited his wife at the hospital on Wednesday, while media from around the world camped outside, seeking any news on the royal pregnancy.
Officials from St. James's Palace have said the duchess is not yet 12 weeks pregnant with the couple's first child.