Under the offer, which was launched last September, a couple earning £200,000 between them are able to access 30 hours of free childcare, as long as neither are individually earning more than £100,000.
But members of the education select committee are concerned that this means too many affluent families are benefiting from the support when it could be redirected to those most in need. They want government to consider reducing the threshold and redistributing money saved into specialist support for disadvantaged children.
Questioning Zahawi as part of an inquiry into improving children's life chances, select committee chair Robert Halfon, himself a former Department for Education minister, said: "Can it be right that a couple can earn £200,000 get the 30 hours free childcare when disadvantaged children need support?"
"How can you say your priority is to help the most disadvantaged when actually it is the wealthy who are benefitting from this more than those most disadvantaged groups?"
He added: "How can that be morally right. That's redistribution gone wrong surely?"
But Zahawi criticised the committee's concerns and said that the 30 hours offer was part of a wider strategy that includes offering 15 hours of free early years education to disadvantaged two year olds.
"From what I've seen [the 30 hours offer] is helping the right parents," he said.
"You only have to earn £6,500 as a single parent to be able take advantage of this or as a two parent £13,500. It is working.
"We can always make it better. But the faux outrage of ‘how can this be right' I don't agree with I'm afraid. We are doing the right thing."
Zahawi did add that the 30 hours offer will be subject to a one-year review, which will cover all aspects of the policy, including thresholds.
Analysis by the London School of Economics released last month concluded that government free early hours initiatives are disproportionately helping children from affluent homes.
Their research said that the 30 hours initiative would widen the social mobility gap between rich and poor children.