The Australian station 2DayFM placed the recording of the conversation on its website.
Australian radio personalities Mel Greig and Michael Christian later apologized 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.