The woman was bitten and scratched by a ringtail possum in Sydney's north in early March, and developed symptoms including swollen lymph glands, fatigue, and a sore throat, NSW Health said in a statement.
Testing is ongoing to confirm the diagnosis of tularaemia.
"If you see sick or injured wildlife, do not pick it up or try to rescue it. Instead, contact the experts at your local licensed wildlife care group or local veterinarian," NSW Health's acting director of communicable diseases Keira Glasgow said.
Tularaemia is an extremely rare bacterial disease which can be transmitted to humans from infected animals but cannot be transmitted between humans, NSW Health said.
The disease is highly contagious but most people recover fully with appropriate antibiotics, Ms Glasgow said.
Symptoms appear within a fortnight of exposure to the bacteria and include fever, chills, fatigue, body aches, headache and nausea.
Those exposed to the bacteria through bites and scratches to their skin will also develop an ulcer at the wound.
"If you have become unwell with these symptoms after recently touching a possum, especially if you were bitten or scratched, it is important to seek medical treatment early," Ms Glasgow said.
Just two cases have previously been reported in Australia, both of whom had been bitten or scratched by possums in Tasmania in 2011.
Don't touch possums... Source: San Diego Zoo
The infection has only been found in two possums in Australia, which died in 2002 and 2003 in separate clusters.
There have been no deaths in Australia associated with tularaemia and the type of bacteria present in Australia is less virulent than that seen in North America, NSW Health said.
The Taronga Conservation Society's Australian Registry of Wildlife Health is helping the NSW Health investigation.
