The women were from Australia, New Zealand, the UK and France.
A statement was issued by Qatar’s government communications office amid continuing outrage following the 2 October incident, which has spiralled into a public relations catastrophe for the Gulf state that will host the 2022 football World Cup, with Australia and New Zealand expressing their anger over what happened.
In the statement, Qatar described the abandoning of the baby as "attempted murder".
"The subsequent procedures taken by the authorities at the airport, including examining a number of female passengers, revealed that standard procedures were violated," the statement said. "Those responsible for these violations and illegal actions have been referred to the Public Prosecution Office."
It added that an investigation by Qatari authorities was continuing and that Sheikh Khalid bin Khalifa bin Abdulaziz Al Thani, the country's prime minister and interior minister, offered his country's "sincerest apology" to the women forced to undergo the exams.
"What took place is wholly inconsistent with Qatar’s culture and values," the statement said.
“Qatar is fully committed to the safety and security of all travelers.”
It is not clear how many people could be prosecuted, nor how senior they might be.
The physical examinations of passengers bound for Sydney and nine other unnamed destinations triggered outrage when it was first reported in Australia, where the government denounced the searches as inappropriate and beyond circumstances in which the women could give free and informed consent.
Rights activists say such exams conducted under duress amount to sexual assault.
In a statement on Thursday, New Zealand’s foreign ministry said the action was "completely unacceptable".
“We were extremely concerned to learn... that a New Zealand national was involved in the appalling incident involving female passengers on several Qatar Airways flights,” it said.
As the reports came to light this week, the government of Qatar apologised and promised a full investigation to be shared internationally. It earlier called the discovery of the newborn buried in a plastic bag under trash "an egregious and life-threatening" act.
In Qatar, like much of the Middle East, sex and childbirth outside of marriage are criminalised. Migrant workers in the past have hidden pregnancies and tried to travel abroad to give birth, and others have abandoned their babies anonymously to avoid imprisonment.