After they displayed cold-like symptoms, tests revealed the chimps had contracted the respiratory syncytial virus (RSV).
Zoos SA chief executive Elaine Bensted said it was the first time RSV had been detected in Monarto's chimps.
It is the most common cause of bronchiolitis and pneumonia among infants under one year of age and is usually spread when an infected person talks, coughs or sneezes.
Ms Bensted told ABC radio the virus would have been picked up from a visitor to the park, but it was unlikely the precise source of the infection would ever be known.
The zoo said the two chimps of most concern were males Enzi and Tsotsi.
Enzi's condition improved on Sunday and he had started playing again.
"Tsotsi is still very poorly but more willing to move around," the zoo said.
"He has eaten some high-value foods including bananas and pineapple and has had to drink. All good signs."
"Vets are hopeful Tsotsi has turned a corner but still has some way to go before he is back to his old self."
The other chimps have runny noses and coughs but are otherwise coping well and acting fairly normally.
The keepers and life sciences team who care for the troop will continue to wear full personal protective equipment including masks.
Ms Bensted said it was hoped the chimpanzee exhibit could be reopened at some stage this week.
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