The woman chose to abort the 32-week foetus but staff injected the wrong twin.
The hospital in Melbourne described it as a "terrible tragedy".
"The Royal Women's Hospital can confirm a distressing clinical accident occurred on Tuesday," it said in a statement.
"We are conducting a full investigation and continue to offer the family and affected staff every support."
The woman went on to have an emergency caesarean to end the life of the sick foetus.
'Thorough investigation' Victorian Health Minister David Davis said the hospital investigation would be overseen by an independent expert.
"I am very much determined to get to the bottom of what went wrong," he said.
State Premier Ted Baillieu echoed his sentiments, saying: "I don't think it's appropriate for anybody to draw any conclusions other than this is a horrible tragedy.
"We'll make sure that the investigation is as thorough as it can be."
In a brief statement, the family asked for privacy "at what has been a very difficult time for us".