The cartoon, by prominent artist Jonathan Shapiro, known as Zapiro, also features a poem, which refers to Mr Zuma as a "dick".
The latest row comes just weeks after the ANC forced an art gallery to withdraw a painting showing Mr Zuma with his genitals exposed.
Mr Zuma is set to face Zapiro in court in October over a different cartoon.
The president sued the cartoonist, who works for the Mail & Guardian newspaper, after he depicted Mr Zuma in 2008 about to rape a female figure representing justice. Mr Zuma was cleared of raping a family friend in 2006.
The pair have also clashed over Zapiro's portrayal of Mr Zuma with a shower cap on his head - a reference to Mr Zuma's statement in the rape trial that he had taken a shower after having sex to reduce the chance of contracting HIV.
"We find it unacceptable and shocking that after the harsh experiences that South Africa, the president and his family has experienced few weeks ago, that Zapiro and the Mail & Guardian will find it appropriate to continue with the insults and hurt to the president, his family and the broader ANC constituency," the ANC said in a statement.
"All South Africans share our disgust."
The painting in the gallery triggered a huge debate in South Africa about the freedom of expression and the right to privacy.
Before the gallery agreed to remove the painting, called The Spear, it was vandalised by two men.
In an affidavit, Mr Zuma said: "The portrait depicts me in a manner that suggests I am a philanderer, a womaniser and one with no respect."
Mr Zuma, who has four wives, has previously sued local media companies 11 times for defamation.
South Africa's governing ANC has expressed its "disgust" at a cartoon of President Jacob Zuma as a penis.