Turei said she did not know the woman's name or details. Regardless, she would never abuse the trust of those who disclosed information to her, she said.
"I am supporting her in her choices to be the best possible mother that she can be and find the best possible of welfare that she can.
"I will never condemn a beneficiary for working as hard as they can to put food on the table and a roof over their head."
While Turei said she could not condemn those who lied to Winz to protect their children, she did not go as far as saying she would encourage beneficiaries to cheat the system.
Turei challenged Ministry of Social Development Minister Anne Tolley in Parliament about her ministry's treatment of people on welfare.
She cited the large number of people who had spoken out in the last week about "denigrating" treatment at the hands of MSD and asked whether the minister would consider an amnesty so they could discuss their entitlements without risking investigation or financial punishment.
Tolley did not directly answer her question, but said there was "no doubt" that it was difficult to manage on a benefit.
"That is why the staff at Work and Income work so hard to help them into sustainable employment because it's the best way out of poverty."
The Green Party has promised to scrap all sanctions and work obligations for beneficiaries if it comes into power.
In announcing the policy at the party's AGM last week, Turei revealed that she had lied to Winz 20 years ago about her living situation to avoid losing her benefit.