UK Director of Care for the Family, Kathryn Hill believes Sir Michael Wilshaw's proposals would only penalise the "people who could least afford it."
Sir Michael, the head of education watchdog, Ofsted has also claimed poverty is too often used as an excuse for educational failure among white working-class families.
Speaking to The Times Sir Michael said: "I was absolutely clear with parents - if they weren't doing a good job I would tell them so. It's up to head teachers to say quite clearly, 'You're a poor parent.'
"If parents didn't come into school, didn't come to parents' evening, didn't read with their children, didn't ensure they did their homework, I would tell them they were bad parents.
"I think head teachers should have the power to fine them. It's sending the message that you are responsible for your children no matter how poor you are."
Care for the Family's Katherine Hill told Premier's Des Busteed on the News Hour why she doesn't support Sir Michael's idea.