Mr Balls announced on Thursday that it is now compulsory for all 15-year-olds to take part in at least one year of sex and relationships lessons.
Until now, parents had the right to withdraw their children from lessons about same-sex relationships, sexually transmitted diseases, abortion and contraception up to the age of 19.
Now children opting out of sex education classes will be regarded as truants and their parents could face a fine or prosecution.
The Catholic Education Service in England and Wales said it was “disappointed” that a “blanket withdrawal” could no longer apply but added that it was pleased that the right of withdrawal from sex education lessons would remain up to the age of 15.
“We continue to wholeheartedly support the belief that parents are the first educators of their children, as well as recognising the significant roles and responsibilities of governing bodies on these issues,” it said.
It continued: “CESEW will continue to firmly uphold the position that parental rights remain vital, particularly but not exclusively, in those most formative and critical years up until the age of 15.
“As age and growing independence brings young people ever closer to pressures, advertising and coercion to behaviour which can undermine the healthy life of young people, we are comforted in the knowledge that our schools and colleges will do an exceptional job in providing Sex and Relationships Education, set within the teachings of the Catholic Church.”
CESEW added its support for the continued legal right of schools to determine the content of what is taught in personal, social and health education (PSHE) within their schools and that governing bodies retain the right to determine what is taught in line with the ethos of the school.