The mistake at Melbourne's Royal Women's Hospital on Tuesday has left the twins' family in shock and numerous questions over how such an error could occur.
The woman carrying the twins had decided to abort one of them on the advice of doctors who told her the baby had a congenital heart defect which would seriously threaten his survival.
Despite earlier checks by an ultrasound technician, the wrong baby was terminated.
The baby with the heart problem was also then terminated after the mistake was uncovered.
Victorian Health Minister David Davis yesterday foreshadowed as many as three inquiries into the mishap and flagged the potential for compensation for the affected family.
He said the hospital would hire a senior interstate clinician to investigate what happened and the Consultative Council on Obstetric and Paediatric Mortality and Morbidity would also review the incident.
The council provides advice to the Health Minister of the day on perinatal, maternal and pediatric morbidity and mortality issues.
Mr Davis also said that Health Services Commissioner Beth Wilson would be involved to assist the family on conciliation and other issues, analysing what happened and how the family could be helped.
This could include possible compensation.
"There's no question that this is an incident that everyone would have preferred had not occurred," Mr Davis said. "And, indeed, may need very, very thorough investigation."
The hospital has apologised for the error.
"This is a terrible tragedy and the hospital is deeply sorry for the loss suffered by the patient and her family," a spokeswoman said. "We are conducting a full investigation and continue to offer the family and affected staff every support."
The family yesterday issued a brief statement requesting privacy in their grief.
Ms Wilson said the investigations should aim to prevent similar tragedies.
"It doesn't sound like it's some terrible systemic error; it just sounds like it's one of those ghastly mistakes that human beings sometimes make, unfortunately," she said.
"I don't have any clinical information on this particular case, but there is no such thing as a medical procedure that doesn't involve some risk.
"I guess the existence of two fetuses in these circumstances does mean that there is a risk."