Women on board a flight bound for Sydney, including 13 Australians, were forced to undergo invasive internal examinations earlier this month after a premature baby was found in an airport bathroom.
Foreign Minister Marise Payne has raised the incident with the Qatari ambassador.
"This is a grossly, grossly disturbing, offensive, concerning set of events," Senator Payne told reporters in Canberra on Monday.
"It is not something I have ever heard of occurring in my life, in any context."
Because of coronavirus rules, the ambassador could not be summoned to federal parliament.
Instead, the minister has spoken to the ambassador over the phone to reiterate the government's concerns, which were first raised on October 6.
Senator Payne expects Qatari officials to conduct an urgent investigation and hand over its report by the end of this week.
She confirmed the matter had also been referred to the Australian Federal Police.
The federal government said the examinations went far beyond circumstances in which the women could give free and informed consent.
"The Australian government is deeply concerned at the unacceptable treatment of some female passengers on a recent Qatar Airways flight at Doha Airport," a spokesman told AAP.
"The government has formally registered our serious concerns about this incident with Qatari authorities. The Department of Foreign Affairs and Trade is engaged on this matter through diplomatic channels."
Hamad International Airport management said the baby was safe and being cared for by medical and social workers.
Medical professionals were concerned for the mother's health after the infant was found and had requested she be located.
"Individuals who had access to a specific area of the airport where the newborn infant was found were asked to assist in the query," airport management told the ABC.
Labor leader Anthony Albanese described the reports as disturbing and said the government was right to demand answers.
"The idea that women could be subject to these very intrusive searches is, in my view, an absolute disgrace," he told reporters.
"The government needs to really make the strongest possible protest to the government of Qatar."
Federal opposition frontbencher Joel Fitzgibbon said the government should be robust in its response.
"If true, this effectively amounts to state-sanctioned sexual assault and we should all be very, very concerned," he told the Seven Network.
Nationals MP Barnaby Joyce said it was outrageous and completely unacceptable the women were subjected to such humiliating examinations.
