"The Spear," a painting by Brett Murray, shows a clothed Zuma standing in a defiant pose, with his penis and scrotum clearly visible. Since there is no literal spear shown in the painting, viewers can assume that the title is a phallic reference.
Zuma is launching a court case this week in which he argues that the painting violates his right to dignity, according to reports.
The work "has the effect of impugning my dignity in the eyes of all who see it. In particular, the portrait depicts me in a manner that suggests that I am a philanderer, a womaniser and one with no respect," said Zuma in a legal affidavit cited by Britain's Guardian.
He is asking a court to remove the painting from public display.
The painting is being shown as part of a solo exhibition of Murray's work titled "Hail to the Thief II" at the Goodman Gallery in Johannesburg. The show features a number of politically satirical works that are intended "to humorously expose the paucity of morals and greed within the ruling elite," said the gallery on its website.
Further fanning the flames of controversy is the fact that the artist is white and the president is black. Zuma's supporters say that the painting is crude and humiliating, and uses racially stereotypical imagery.
"The Spear" is about 6 feet tall and little more than 4 feet wide.
Zuma took office in 2009 and is a member of the African National Congress. He is ethnically Zulu and is a polygamist, having been married several times and fathered numerous children.
South Africa is a constitutional democracy where the freedom of speech is protected.
The South African newspaper City Press ran a copy of the painting in a recent edition and on its website. Zuma is also trying to have the newspaper remove the image from its site, but the editorial leaders have so far refused.