The two were in custody at the Rosebank police station after they allegedly painted over the artwork.
Greg Palmer, attorney for the Goodman Gallery which is hosting the exhibition by artist Brett Murray, said the gallery would lay charges of destroying private property against them.
Earlier a television journalist working on a story about the painting, titled The Spear, told how she tried to stop the older man from damaging the work.
Iman Rappetti, eNews channel anchor, was in the Goodman Gallery in Rosebank, close to the work when the man took out a pot of paint and marked an X across the genital area of the portrait.
She said she grabbed him, while shouting to gallery staff to come and help her.
"It was surreal."
Completely ordinary looking
Rappetti described the vandal as a completely "ordinary" looking critic wearing a tweed jacket. Unbeknown to Rappetti the teenager was standing behind her with a large pot of black paint.
The youngster started "going to town on the picture", she said.
"I was screaming."
Gallery staff apprehended both the man and the youth. The police arrived shortly afterwards and took them away.
Rappetti said the gallery staff told her the first man had identified himself as an Afrikaans journalist. He had visited the Goodman Gallery before.
"He did not sound Afrikaans to me," she said.
The public and reporters crowded outside the gallery, which was closed.
Inside the gallery gate were three private and armed security guards wearing bulletproof vests - with one guard carrying a rifle.
*Sapa reported earlier the one suspect's age as 15. We cannot confirm his age at this stage.