The posts have caused an outcry on social media, with scores of people coming out to slam racism and defend Dlamini-Zuma.
ANC deputy secretary-general Jessie Duarte on Friday night issued a video also slamming Herselman.
Duarte called Herselman a racist who had absolutely no respect for human beings or human life.
In a statement on Saturday ANC spokesperson Pule Mabe condemned the attack on Dlamini-Zuma, saying the comments were “racist, sexist and misogynistic”.
“We view this as a gross human rights violation and add our voice to the calls made by the ANCWL for both the Human Rights Commission and the SA Police Service to immediately investigate and take appropriate action on this matter,” said Mabe.
The ANC called on its members to be prepared to resist vicious personal attacks on Dlamini-Zuma both on social media and also by opening charges of hate speech.