Immediately following the the girl's diagnosis the main water temperature for the hospital was raised to kill off possible sources, and potential sources of warm water were checked.
Children in the hospital with poor immune systems have been advised to not use the showers as an extra precaution.
The girl is receiving intensive treatment. She was admitted to Starship several months ago with a "severe underlying illness" and poor immunity. She had further testing after developing a serious chest infection last week.
"In this particular case we identified the Legionella as the likely cause of the chest infection," Dr Aickin said.
"I was very concerned because I knew that this is an environmentally acquired organism and it's been acquired in the hospital. This child is quite vulnerable from the underlying condition."
The organism is acquired from the environment and the patient had not been outside the hospital during the 2-14 day incubation period.
The girl was isolated and nearby patients from the ward she had been in were tested, all returning negative results.
"The usual incubation period has passed without a second case being identified, so staff are confident it is an isolated case," Dr Aickin said.
Details about the case were first released to those potentially affected, then the general public.
Legionella bacteria requires still, warm water to grow. A person can become infected after breathing in the water vapour.
The elderly and patients with poor immunity are particularly at risk.
Symptoms can include fever, rapid breathing and the need for additional oxygen. In several cases a patient might require ventilation and intensive care treatment.
The water system to Starship Hospital is being reviewed as part of an investigation. A monthly test for Legionella in the hospital water system returned a negative result about February 12, said Dr Aickin.