Nurse Jacintha Saldanha was found dead on Friday, three days after taking the call from Australian radio station 2Day FM.
The Australian Communications and Media Authority (ACMA) will focus on the 2Day FM license holder and not directly on the presenters who made the prank call.
It will be examining if “broadcasting obligations” were breached.
On Wednesday, speaking in the Commons, UK Prime Minister David Cameron called Jacintha Saldanha’s death a “complete tragedy” and said lessons needed to be learnt.
Jacintha Saldanha had taken a call from presenters Mel Greig and Michael Christian, who were pretending to be the Queen and Prince Charles, at the King Edward VII’s Hospital, where the duchess was being treated for severe morning sickness.
ACMA said its investigation would look at the compliance of 2Day FM’s licensee, Today FM Sydney Pty Ltd, with its license conditions and the Commercial Radio Codes of Practice.
ACMA chairman Chris Chapman said: “The ACMA’s formal regulatory relationship is always with the relevant licensee, and not the presenters of any broadcast in question. The ACMA will be examining whether the licensee has complied with its broadcasting obligations.”
Under Australia’s Broadcasting Services Act, radio and television licensees have primary responsibility for ensuring that the material they broadcast reflects “community standards”.
Jacintha Saldanha, 46, answered the call from the 2Day FM presenters in the early hours of the morning on 4 December and, believing them to be members of the Royal Family, put them through to another nurse who gave a detailed update on the duchess’s condition.
She was found dead three days later at staff accommodation close to the hospital.
Southern Cross Austereo, which owns 2Day FM, said all profits from advertising on the station for the rest of the year would go into a fund for Jacintha Saldanha’s family.
MP Keith Vaz, who met Jacintha Saldanha’s family in Parliament on Monday night, has called on the hospital where she worked to hold a full inquiry.
He has also written to Southern Cross Austereo’s chief executive Rhys Holleran, expressing concern that the company had “not taken any steps to assist the family”.
“There has been no written apology, no request for a meeting with the family and no attempt to travel to the United Kingdom to express contrition,” he wrote.
Scotland Yard said the results of a post-mortem examination on Jacintha Saldanha would be released on Thursday morning at an inquest into her death.
The death is not being treated as suspicious and the inquest hearing in London is expected to be opened and adjourned as inquiries are continuing.
The two presenters involved in the hoax call, Michael Christian and Mel Greig, have said they are “gutted and heartbroken” over the death of Jacintha Saldanha.
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