Liz Truss, who is chief secretary at the Treasury, told Sophy Ridge on Sunday that she was "absolutely appalled" by Sir Christopher Chope after he blocked a move to give courts more powers to protect children at risk of female genital mutilation.
Sir Christopher shouted "object" as the proposed law was read out for debate on Friday - halting its progress on the way to becoming statute.
The backbench MP caused uproar last year after using the same tactic to block a bid to make "upskirting" a specific criminal offence.
He faces the ire of cabinet ministers, with Home Secretary Sajid Javid saying he was "very disappointed" and Health Secretary Matt Hancock calling the move "outrageous".
But Ms Truss went one step further, vowing to confront Sir Christopher personally to ensure he "changes his mind".
"I was just absolutely appalled, because we know there has only been one conviction against somebody for female genital mutilation," she told Sky News.
"This is an action that harms the lives of girls, this is happening in our country in the 21st century, I find that appalling and we need to do much, much more to stop it.
"When I see one of my colleagues opposing a measure that could have saved girls' lives, could have saved girls from that horrendous experience, I am absolutely appalled by that."
Asked whether she was ashamed to be in the same party, Ms Truss said: "Well I am going to be speaking to him this week, I want to see him change his mind.
"I want to see the Conservative Party make sure that we show that is completely unacceptable."
The law change would have handed courts the power to give local authorities shared parental responsibility for a child at risk of FGM.
Explaining why he blocked the law on "upskirting", Sir Christopher previously told the Bournemouth Echo: "The government has been hijacking time that is rightfully that of backbenchers.
"This is about who controls the House of Commons on Fridays and that's where I am coming from.
"The government is abusing parliamentary time for its own ends and in a democracy this is not acceptable.
"The government cannot just bring in what it wants on the nod. We don't quite live in the Putin era yet."