The actual painting that was on show at the Goodman Gallery in Johannesburg was vandalized by protesters on Tuesday.
The African National Congress said it was “rude, crude and disrespectful” and wanted all images of the painting online and elsewhere taken down.
Its challenge is expected to be heard by judges shortly.
The South Gauteng High Court is due to deal with the case against the gallery and the City Press website.
The Spear, a $14,000 acrylic painting by Brett Murray, an artist known for his political and provocative work, has already been sold.
The case is seen as a choice between freedom of expression and the right to dignity, both of which are protected in South Africa’s constitution.
The ANC is supporting President Jacob Zuma’s bid to have the painting removed from public view, whether in real or virtual form.
It called on people backing the president to go to the court and show their support.
Party spokesman Jackson Mthembu told the Sapa news agency: “A lot of people are coming to defend the image of the ANC and Msholozi [Zuma].
“Millions and millions are offended, and those millions are not necessarily black people only. They find it insulting.”
On Tuesday, two men went into the gallery and defaced the painting, daubing a red cross on it and smearing it with black paint.
Barend la Grange and Louis Mabokela appeared in court briefly on Wednesday, along with George Moyo who is accused of trying to spray-paint the word “respect” on a gallery wall.
In an affidavit served on the City Press newspaper, Jacob Zuma said he was shocked by the work saying: “The portrait depicts me in a manner that suggests I am a philanderer, a womanizer and one with no respect. It is an undignified depiction of my personality and seeks to create doubt about my personality in the eyes of fellow citizens, family and children.”
President Jacob Zuma, who has four wives, has sued local media companies 11 times for defamation. Some cases have been settled, others dropped, but most are outstanding.
The best-known case is a 2008 suit against one of the country’s most high-profile artists, Zapiro, after he depicted Jacob Zuma about to rape a female figure representing justice – this is due to be heard in October.
Jacob Zuma was cleared of raping a family friend in 2006.
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