An investigation is under way at an Australian hospital after staff treating a woman carrying twins accidently terminated a healthy 32-week-old foetus.

Doctors at the Royal Women's Hospital in Melbourne had told the woman that one of her babies had a congenital heart defect that would require years of operations, if he survived.

The woman decided abort the foetus, but staff accidently injecting the wrong baby, terminating the healthy twin.

"The Royal Women's Hospital can confirm a distressing clinical accident occurred on Tuesday," The Royal Women's Hospital in Melbourne said in a statement.

"This is a terrible tragedy and the hospital is deeply sorry for the loss suffered by the patient and her family. We are conducting a full investigation and continue to offer the family and affected staff every support."

The woman went on the have an emergency caesarean to end the life of the sick foetus.

"She went to the hospital with two babies and now she has none," a friend of the woman told the Herald Sun newspaper.

"And she had the heartache of giving birth to her sick baby. She's traumatised."

Medical staff who were involved in the accident had been described as "inconsolable" because of the events.

Victorian state Premier Ted Baillieu told reporters it was a tragedy for everyone involved.

"I don't think it's appropriate for anybody to draw any conclusions other than this is a horrible tragedy," he said.

"We'll make sure that the investigation is as thorough as it can be."