A second baby is in a critical condition
New South Wales health minister Jillian Skinner has apologised after the discrepancy was discovered when a paediatrician raised concerns.
She said: "I am profoundly sorry for the families of a newborn who died and another newborn who was severely affected.
"I deeply regret these families have suffered through such a devastating error. NSW Health will do all it can to support them."
The grieving families - whose children were born in June and July this year - were told about the mistake at the weekend.
Eight operating theatres at the hospital have since been checked but the one affected remains closed. Staff have confirmed that these are the only two incidents that they are aware of since the gas tanks were installed in July 2015.
The website of the company who installed the tanks, BOC Ltd, suggests its oxygen gas tanks are black, while those filled with nitrous oxide are light blue. NSW health's legal representatives have written to the company demanding to know how such a fatal error could occur.
South Western Sydney Local Health District has launched an investigation to find out if hospital staff followed rules that may have uncovered the installation error last year.
Other health facilities in the region have been asked to check their gas outlets and review protocols for ensuring they are properly installed.