The Cape Times reported that Sakeenah Dramat, 16, and her brother Bilaal, 13, were asked by teachers at Eben Donges High in Kraaifontein to remove their headscarf and fez on the first day of school last week.
Their mother Nabila said the school called her later in the day and said it was against the code of conduct for her children to wear the headgear.
The children had since missed six days of school.
"I can't allow them to take it off because it is against our Islamic beliefs.... It is very sad. It is very disturbing. They are heartbroken to be out of school for such a simple reason."
The SAHRC said it was investigating the case. School principal Wilfred Taylor asked the newspaper to contact the provincial education department for comment.
Department spokesman Paddy Attwell told the newspaper an official would meet the parents at the school later on Thursday to arrange the children's return to school.
"According to the [national school uniforms] guidelines, schools should take religious and cultural diversity into account. We believe it is a simple matter to adjust dress codes to meet these requirements," he said.