Zapiro's latest cartoon is a "vulgar portrayal" of President Jacob Zuma, lobby group AfriForum said on Monday.
The cartoon was "a vulgar portrayal of the president [and] unproductive and in poor taste." AfriForum spokesperson Ernst Roets said in a statement.
The cartoon by Jonathan Shapiro depicts an erect penis with a showerhead and legs standing before a mirror with an accompanying limerick about Zuma.
It was published in the Mail & Guardian on Friday.
Roets said the cartoon did not contribute towards finding a solution to South Africa's problems.
"AfriForum is of the opinion that controversial issues in South Africa must be approached constructively and that it does not contribute to finding a solution when other people's cultures are insulted in the process."
Roets said although AfriForum supported freedom of speech and artistic experience, this cartoon called into question the matter of dignity.
He suggested artists "evaluate the possible consequences of their work before displaying it to the public".
On Friday, the government called for the removal of the cartoon from the Mail and Guardian website.
Spokesperson Jimmy Manyi said the cartoon was a "defamatory attack" on Zuma's character and violated his rights to dignity as enshrined in the Constitution.
SA Communist Party spokesperson Malesela Maleka called it "B-grade schoolboy lavatory stuff, unworthy of a once talented cartoonist and unworthy of a newspaper that pretends to be serious".
The African National Congress found it "unacceptable and shocking", while its Women's League condemned it.
"The Zapiro cartoons rely on their shock value to make an impact, but calling the president of this great nation a 'dick' is unacceptable..." ANC Women's League spokesperson Troy Martens said.
Responding to criticism of the cartoon, Shapiro said on Friday the public should have the democratic right to be irreverent about leaders, especially those who "display hypocrisy".
"My latest cartoon is meant to be scathing but humorous," he said in an email, issued by his office, to Sapa.
"It's also serious commentary about a seriously flawed, hypocritical leader."