The ANC Women's League has condemned Zapiro for his latest cartoon.
"[Jonathan] Shapiro has taken his attempts at satire too far," the league said on Friday.
In his cartoon, Zapiro drew an erect penis with a face and legs and a showerhead on its head looking at itself in a mirror.
The signature of artist Brett Murray is in a bottom corner of the mirror and the name of the Goodman Gallery also appears in the cartoon.
Under the heading "The Spear to be raised at Social Cohesion Summit", he includes a poem referring to Zuma, which the league felt was an insult to people who suffered under apartheid.
The league said Shapiro showed disregard for the "healing process" under way in South Africa.
The Spear is a painting, now defaced, by artist Brett Murray, which featured a depiction of Zuma with his genitals exposed.
In addition to a court application to have it removed, the ANC led a march to the Goodman Gallery to register its protest.
"The Zapiro cartoons rely on their shock value to make an impact, but calling the president of this great nation a 'dick' is unacceptable and the [league] would like to know who the 'we' he is referring to in the cartoon actually is, as the majority of the population who voted for the president clearly did not think this of Zuma."
The cartoon was an attempt to fuel divisions in society and was a violation of the president's dignity, the league said.
"The right to freedom of expression is a right enshrined in the constitution, a constitution pioneered by the ANC, however this right is not absolute and one must always remember a founding principal of our Constitution is the right to human dignity, which was denied to so many during apartheid." – Sapa