The woman, aged in her forties, is also in a critical condition.
Bystanders were first on the scene after finding the three children and the woman with stab wounds inside a vehicle in the Blue Mountains, west of Sydney, on Sunday afternoon.
One young child died at the scene despite witnesses rushing to help, delivering first aid while waiting for emergency services to arrive.
The alleged domestic violence incidence came at the end of a horror weekend across NSW, after three women were allegedly murdered inside their homes within a 12-hour period on Saturday.
NSW Police Deputy Commissioner Peter McKenna described the past two days as devastating.
"It's a horrific and tragic weekend and it's like one that I don't remember in my career," he told Nine's Today.
"When you balance out those three and plus the no-more-tragic situation than we had in the Blue Mountains. Put them all together and it's unfathomable."
Paramedics treated all three at the scene on Sunday before taking them by road to Westmead Hospital and Westmead Children's Hospital in critical condition, where they remain.
"The two children and their mother are in a critical condition," Mr McKenna said.
"The mother is the suspect in this matter, for domestic related homicide, and that investigation is ongoing."
Hours after the incident, NSW Police Superintendent John Nelson said the father of the children had been notified.
The father had been at work when he received the call from police, he said.
"You can imagine receiving that tragic news," Supt Nelson told reporters.
He said the woman had not previously come to the attention of police and that investigators were not looking for anyone else in relation to the incident.
The woman is aged in her 40s and the children are all under five years old.
All three have undergone surgery in hospital.
Supt Nelson praised the efforts of the "upstanding" members of the public who responded to the tragic scene.
"People are just going about a lovely Sunday afternoon and being confronted with this is traumatic and tragic for anybody," he said.
Responding officers would not be spared the hardship and would have access to available supports.
Police said the weapon used and the circumstances surrounding the incident would form part of investigations.
Blue Mountains councillor Darren Rodrigo on Sunday described the news as "absolutely horrendous and tragic".
"Our deepest love and condolences to the immediate family and our prayers with all the children involved," he said.
"A massive thank you to the community members (who) intervened to provide medical assistance and to our first responders for their incredible support and courage during this time."
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