A tragic hospital mix-up in Melbourne has seen a mother lose both of her unborn twins.

The woman was told by doctors at the Royal Women's Hospital, one of her twin boys had a heart defect and may not survive.

She made the decision to abort the sick baby on her doctors' advice.

But the wrong baby, the healthy foetus, was terminated.

The mother then had to undergo emergency surgery to remove the sick child.

The hospital has apologised and promised a full investigation.

Photo:Getty/Getty Images News/Sean Gallup/Staff