The nurse was found dead Friday morning at a residence near King Edward VII Hospital where she worked, The Independent reported.
Paramedics were sent to the scene but were unable to revive the woman. Scotland Yard said it is treating the death as a possible suicide.
The pranksters asked about Middleton's condition and the nurse passed the call along to a colleague who gave out private information on the duchess of Cambridge.
After the incident, John Lofthouse, chief executive at the King Edward VII Hospital, said: "This was a foolish prank call that we all deplore. We take patient confidentiality extremely seriously and we are now reviewing our telephone protocols."
The Sydney Morning Herald reported the two pranksters, Mel Greig and Michael Christian, would be off the air at 2Day FM until further notice.