South Australia Health said the child, from Adelaide, has an invasive strain of the disease identified as serotype W.
Fifteen people have been identified as close contacts of the baby.
This is the fourth case of invasive meningococcal disease reported in the state this year. This compares to two cases recorded at the same time last year.
SA Health said of the four cases, two are serogroup B and two are serogroup W.
Symptoms include nausea, vomiting, neck stiffness, headache, joint pain, sensitivity to light, or a sudden fever.
A rash of red-purple spots or bruises is often seen with the illness but in some cases a rash doesn’t appear, or it could be the last symptom to appear.