He also accused some working class families of no longer valuing education as a way of improving their family's prospects.
And the Ofsted chief said some TV programmes such as Shameless, a Channel Four comedy drama featuring a family on a Manchester housing estate glorified bad parenting.
He said: "It's almost glorifying fecklessness."
In an interview with The Times, Sir Michael said social deprivation was used too often as an excuse for underachievement.
Referring to his time as a headteacher at inner London schools, 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 headteachers 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 that they were bad parents.
"I think headteachers should have the power to fine them. It's sending a message that you are responsible for your children no matter how poor you are."
He said poor white working-class children are the lowest performing group in England's schools.
In contrast, he said many pupils from immigrant families were doing 'astonishingly well' in some parts of the country, boosting Britain's position in international league tables.
What do you think? Are you tired of the constant talk of 'bad' parents and fines when the vast majority of us do everything we can to support our children at school while also working and looking after younger children?