The Goodman Gallery, where a controversial painting of President Jacob Zuma is housed, was temporarily closed to the public on Tuesday.
Gallery owner Liza Essers said the move was prompted by numerous threats and a defacing incident.
“The extent of the rage has astonished me and upset me very much,” she said in a statement.
“We have decided to do this as we feel that the Goodman Gallery, its staff, as well as public visitors are at risk.”
The painting by Cape Town artist Brett Murray, which depicted Zuma with his private parts exposed, was defaced by two people visiting the gallery.
The High Court in Johannesburg will hear the ANC's application to have the painting taken down on Thursday.
“Charges of malicious damage to property have been laid against the suspects who defaced the painting, and we have removed the painting from the premises to a safe location, pending the court case,” said Koseff.
A third person was arrested outside the premises.
Essers said the painting - “The Spear” that is part of Murray's exhibition “Hail to the Thief II” - had generated a debate that clearly engaged with important legal and constitutional issues.
“I furthermore never imagined that this debate would transform into harmful physical action,” she said.
“This is over and above questions of political power, which formed part of its original dialogue.”
The gallery said it had recognised how “incredibly divided” the country has become about the issues this controversy had raised.
“We are thankful for the support that we have received so far and also reiterate that we did not anticipate the harm that has been caused, or the offence that has been taken,” said Essers.
“We must take cognisance of all responses to our exhibitions, and do not value one opinion above another.”
The painting was defaced with red and black paint, obscuring the face and waist of the figure.
Colonel Vishnu Naidoo confirmed the arrests in a statement.
“The two men, 58 and 25 years of age, allegedly made crosses with red paint and smeared black paint respectively on the portrait.”
The arrests came within an hour of the high court setting down the ANC's application.
The Film and Publication Board will take submissions on Tuesday night from parties, including the gallery, as it reacts to complaints and decides whether the painting should be classified.
Board spokesman Prince Mlimandlela Ndamase said it would go ahead in spite of Tuesday's turn of events, because images of the original picture were still widely available on the internet.
In a statement, Nxamalala traditional leaders from Impendle and Zuma's hometown of Nkandla called for the removal of the art piece, saying it violated the president's dignity and rights.
“We believe that the hard-won freedom of expression should not be turned into freedom of insulting, embracing and promoting personal insults by racist artists.” - Sapa