“The department of state security has confirmed that the photograph is fake,” said spokeswoman Phumla Williams.
She said government found it “extremely” distasteful that a member of the public would manipulate a photograph of Mandela at this time.
“We appeal to members of the public to please behave with the same dignity and respect as President Mandela lies in the state for the third and final day on Friday.”
She thanked those who acted respectfully as they said farewell to Madiba, for playing their part.
Mandela family spokesman Lt-Gen Themba Mathanzima told The Star newspaper that the family was very concerned about the picture.
“We don’t know who did this, but we are going to be asking the government to investigate,” Mathanzima was quoted as saying.
“That picture was definitely not taken with our permission. The family is outraged.”
Mandela died at his home in Houghton, Johannesburg, last Thursday, at the age of 95.
An official memorial service was held at FNB stadium, in Soweto, on Tuesday. He will be buried at Qunu, in the Eastern Cape, on Sunday.
AFP tweeted on Thursday afternoon that the photo was in fact a AFP image of Nelson Mandela closing his eyes at ANC conference in Durban in July 1991.