Neville is expected to be faced with calls to resign after revelations of failed attempts by Victoria's Department of Human Services (DHS) to conduct proper background checks on a known sexual predator before letting a child into his care.
The accused is said to have caged his daughter as a virtual prisoner, raping her almost daily from when she was 11 years old, reports the Herald Sun.
All the four kids bore by the woman, who is now under the care of authorities in a safe house, had health problems when delivered in major hospitals in Melbourne. One of the kids died soon after birth.
Their birth certificates do not hold the name of their fathers, prompting alarms as to why questions were not asked at the time.
The man denied the allegations, but was charged after DNA tests allegedly proved he was the father of her children. He is due to appear in court in November.
Comparisons have been drawn between the case and that of Josef Fritzl, the Austrian man who held his daughter as a sex slave for 24 years and fathered seven children with her.
Minister Lisa Neville told ABC Radio: "I was extremely appalled to see the allegations."
"They are only allegations and are before the courts at the moment and we need to be very careful about how much detail we go into," Neville said.
"I became aware of this from the media today and I don't know what, or if, (there has been) any involvement of the police, the department or other agencies ... over the past 30 years.
"This will be a priority to look into," she added.