As second generation believers, and not converts, the youngsters have a right to be exempt from studying Shi'a Islam at school by producing a letter from the denomination.
CSW said the letters are now being rejected on the grounds that the Church is an "illegal organisation".
It claimed schools are insisting children either agree to study Islam, or go home.
CSW's Chief Executive Mervyn Thomas said: "It is worrying that the education of so many children will be unduly interrupted until their parents agree for them to study a religion different to their own.
"Education is a basic right which Iran has undertaken to guarantee to all of its citizens. Children should not be victimised in an effort to penalise their parents for exercising the right to adopt a religion of their choice.
"Since education is the responsibility of central government, we urge the Special Rapporteur on the right to education and other key international human rights experts to make urgent representations with President Rouhani, with a view to ensuring the country fulfils its national and international obligations to respect the right of the child to education, and particularly to religious education commensurate with the convictions and beliefs of their parents."
A number of leaders in Church of Iran have faced action in recent years - normally linked to evangelism. They often face charges of acting against the state.