NSW Health on Monday evening said the patients were a man from Corowa and a child from Wentworth, both in the NSW-Victoria border region.
The department said the man was in intensive care and the child had been discharged from the ICU but was staying in hospital because of the seriousness of their illness.
Authorities are expecting more cases to be confirmed in the future and several people are undergoing further testing.
Acting Chief Health Officer Marianne Gale urged NSW residents to take steps to avoid being bitten by mosquitos.
“We are working closely with the NSW Department of Primary Industries and other states and territories to determine the extent to which the virus is circulating,” Dr Gale said.
“Unfortunately, our recent wet weather has led to very high mosquito numbers, so we need the community to be particularly vigilant and take steps to avoid mosquito bites.
“We know mosquitoes are most active between dusk and dawn, and we need people planning activities near waterways or where mosquitoes are present to be especially cautious, particularly those in the vicinity of the Murray River and its branches.”
Australia’s acting Chief Medical Officer Dr Sonya Bennett last week declared a national alert over the virus, which is spread through the bite of an infected mosquito and cannot move directly from person to person.
The virus is common in a wide swathe of Asia and the Western Pacific, including India, most of China, Indonesia, Papua New Guinea and Japan.
Recent cases are the first time it’s been identified in NSW in humans or animals, according to NSW Health.
Most humans who contract the virus do not experience any symptoms or only experience mild symptoms like headaches or fever.
But the worst affected may suffer inflammation of the brain, a sudden onset of vomiting, high fever and chills, severe headaches, sensitivity to light, neck stiffness and nausea.
The virus has been confirmed in samples from several NSW pig farms but NSW Health stresses it can not be caught by eating pork or other pig products.