Two men reportedly covered the artwork, which was hanging in the Goodman Gallery, in red and black paint.
The governing African National Congress (ANC) asked the High Court to have the painting, called The Spear, removed from the gallery.
The ANC described it as “rude, disrespectful and racist”, but others have defended the political artist Brett Murray’s right to freedom of speech.
The painting, which was worth £9,000 and painted in Soviet-style, red, black and yellow acrylic, had already been sold.
Television footage showed a man in a suit painting a red cross over the president’s genitals and face, while a younger man in a hooded top rubbed black paint over the painting.
One of the men told the BBC: “I’m doing this because the painting is disrespectful to President Zuma.”
The younger man was reportedly assaulted by security guards at the gallery.
Both men, aged 58 and 25, are due to appear before magistrates on Friday, while Zuma will bring court action against the gallery for showing a painting of the president with his genitals on display.
