A baby in South Australia has been diagnosed with coronavirus after its mum first came down with the illness.

SA Health announced the baby and another new case this afternoon, taking the total number of cases for the state to seven, according to news.com.au.

The baby belongs to a 40-year-old woman who was also diagnosed with the virus after just returning from Iran.

SA Health say the mum and baby are "doing well" in hospital.

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The other case is in a 58-year-old man, who arrived from Taiwan on March 3, at Flinders Medical Centre.

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The 40-year-old woman arrived in Adelaide on March 1 on Malaysia Airlines flight MH139 after a stopover in Kuala Lumpur.

"While this is an anxious time, we are on the front foot in South Australia," Premier Steven Marshall said.

A 24-year-old woman is stable after testing positive yesterday. She was travelling through Europe and may have contracted the disease in Italy.

SA Health is trying to track her movements and who she might have come in contact with.