Eight people identified as close contacts of the newborn, who lives in metropolitan Adelaide, have been given precautionary antibiotics to prevent further spread of the disease.
South Australian health authorities say they are yet to determine which strain of the deadly disease the girl is suffering from.
The baby was last reported to be in a stable condition.
She is the third case in SA in the last month following the death of a 29-year-old man earlier this month.
A a 21-year-old woman was also reported to be in a critical condition earlier in the week.
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