The mother of the four-day-old baby boy had had hepatitis virus for several years and doctors say the child runs a high risk of contracting it unless he is immunised within days.
The New South Wales Department of Community Services (DOCS) took out a Supreme Court order to force the parents to immunise their child, but has so far been unable to locate the couple.
A spokeswoman said the department would have to go back to court Tuesday if the parents were not found.
While vaccinations are not compulsory in Australia, New South Wales state health policy mandates that parents of all babies born to hepatitis B-positive mothers must be offered immunoglobulin for the child within 12 hours of birth and four doses of the vaccine over six months.
The baby's father, a financial adviser, is seeking an injunction against the court order, and is adamant the family will stay on the run indefinitely.
The couple, from Croydon Park, fled their home on Thursday to avoid police and DoCS officers, after refusing to have their newborn son vaccinated at Sydney's Royal Prince Alfred Hospital.
They fear that aluminum in the vaccine could cause their child neurological damage and are confident that the hepatitis virus can be managed effectively without vaccination.
The parents have the support of the anti-vaccination group the Australian Vaccination Network.
The baby's father, who is seeking an injunction against the court order, was adamant the family would stay on the run indefinitely.
One of the doctors who alerted state authorities to the couple's refusal to have the baby vaccinated, Professor David Isaacs from Sydney's Westmead Children's Hospital, said that the child's rights were being ignored.
"If you do not immunise a baby in this situation, you're putting that baby's life at risk," he said.
He said if a baby gets hepatitis B at birth he or she will become a chronic carrier of the virus.
"About a third of those chronic carriers will die young from cancer of the liver or cirrhosis of the liver ... this is a horrible disease," he said.
New South Wales Assistant Police Commissioner Frank Mennilli declined to say whether the parents would be charged once they were found.
"It'll be something that'll have to be assessed once that child is located," he said.