The infant tested positive a day after his 40-year-old mother was confirmed to have the illness, after the pair travelled to Adelaide from Iran via Kuala Lumpur on Sunday, health officials said.
They are both currently in isolation at Flinders Medical Centre but are said to be in a stable condition.
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The second new case on Thursday was a 58-year-old man who travelled from Taiwan to Brisbane, and then on to Adelaide, where he arrived on Tuesday.
He is in isolation at Royal Adelaide Hospital and contract tracing is underway.
The two new cases are the six and seventh to be confirmed in South Australia.
A 24-year-old female is also in Royal Adelaide Hospital in a stable condition after being diagnosed on Wednesday.
She recently travelled through Europe, including Italy, and returned to Adelaide from Abu Dhabi via Sydney on 29 February.
Fourteen South Australians are currently awaiting test results for Covid-19.
Australia has recorded two deaths from the virus, including a 95-year-old woman who died at a hospital in Sydney.
Australia and Japan have joined the list of almost 100 nations now limiting arrivals of people from South Korea.
The director-general of the World Health Organisation has urged all countries to “push this virus back”.
Tedros Adhanom said the epidemic can be pushed back but every country must act with speed, scale and clear-minded determination against the virus.
The new coronavirus, officially named Covid-19, has so far infected nearly 97,000 people worldwide and killed more than 3,300.
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Additional reporting by agencies.