NSW Attorney-General Mark Speakman advised the governor to order an inquiry after she received a petition from prominent scientists in March last year, asking that Folbigg be pardoned.
Folbigg, 54, was jailed in 2003 after being convicted of murdering three of her children and the manslaughter of a fourth.
Mr Speakman announced the inquiry on Wednesday, saying dismissing the petition would not be a proper option.
"But the evidence, clearly in my view, reaches the necessary threshold for some kind of intervention," he said.
"It certainly rises to the level of question or doubt that's referred to in the statute about appeals and reviews in this sort of matter.
"A pardon is not appropriate because the evidence does need to be tested.
"A simple pardon without that open transparent process, it would not be appropriate."
Folbigg is not eligible for parole on her 40-year sentence for another six years.
However, a group of prominent scientists have been calling for her early release, arguing there is no medical evidence she smothered the children.
The petition came after scientists discovered two of Folbigg's daughters had inherited a previously unknown genetic variant from their mother, which could lead to sudden and unexpected infant death.
Her two dead sons also had illnesses, which could have caused them to stop breathing as they slept.
An inquiry upheld Folbigg's conviction in 2019.
The petition to Ms Beazley said the case against Folbigg was entirely circumstantial and the trial and later inquiry was derailed by flawed logic.
"It is based on the proposition that the likelihood of four children from one family dying of natural causes is so unlikely as to be virtually impossible," the petition read.
Evidence before the inquiry, as well as the fresh scientific evidence of genetic mutation, should give any reasonable person doubt that Folbigg killed her four children and deciding otherwise rejects medical science as well as the law, the petitioners argue.
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