Parents have started removing their children from a Schweizer-Reneke primary school in the North West amid protests outside the school.
Netwerk24 noted that the woman was severely traumatised.
The Daily Mail reported that parents of the children were displeased with the teacher's implementation of a segregation policy.
Meanwhile the mother of one of the black pupils has insisted the pupils were told where to sit in the classroom.
"This was meant to be an exciting day for me but it's not", she said.
While other parents were thankful for the picture, the mother was irate when she discovered that her child and three other black pupils had seemingly been isolated.
Another parent said she was "pi**** off" by the picture, saying white parents had been thanking the teacher for the image in the WhatsApp group but no-one had brought up the separation.
The viral picture that led South Africans to label Laerskool Schweizer-Reneke racist, merely captured a moment and was not a true reflection of the school ethos, the school's governing body said on Thursday.
"Why should our children be separated by their race?"
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The school has not responded to requests from the local media for comment.
The teacher posted an image of the four to five-year-olds on their first day at Laerskool Schweizer-Reneke on the school's private Whatsapp group to show parents how they were settling in.
"The union can not be silent when there is a gross violation of rights of learners to receive equal treatment and education".
The Human Rights Commission will be sending a team to the school.
The school is in the north west of South Africa and the regional education board has today launched an investigation.
SAHRC spokesperson Gail Smith said the commission would work closely with the department to investigate the allegations.
Sello Lehari, the provincial Education Minister, said after stopping by the school: "From the information I got from the meeting, it seems that there are a lot of cases here of racism".
"The commission is deeply concerned that instances of discrimination and related intolerance continue to take place within the school system".
Protesters gathered at the school on Thursday morning, many of whom are supporters of South Africa's opposition EFF party according to local media.