The incident follows a deadly newborn "laughing gas" mix-up at another Sydney hospital.
New South Wales Health Minister Jillian Skinner apologised for the incident.
"I`m devastated for them and I`m really sorry that such an incident occurred," she told a budget estimates committee.
A spokesman from the opposition Labor Party said Ms Skinner should be sacked to restore public confidence in the healthcare system.
However, Premier Mike Baird has stood by the embattled health minister in the wake of the hospital incidents.
"Jillian Skinner continues to do a good job in very difficult circumstances," Mr Baird said.
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