President Zuma narrowly survived a vote of no confidence earlier in August, and the incident with the wife of President Mugabe — who is a close ally — is the last thing he needs.
Gabriella Engels, 20, showed off pictures of her injuries on social media after the incident at a swanky hotel in the Sandton suburb of Johannesburg at the weekend.
She had a gaping cut in her forehead which she claimed to have suffered when she was hit by a plug on an extension lead brandished by Mrs. Mugabe.
Although he is 93, Mr. Mugabe retains a vice-like grip on Zimbabwe and last year he was confirmed as the ruling ZANU party's candidate for next year's presidential election.
Mrs. Mugabe, who is 41 years younger than her husband, used diplomatic immunity in a bid to escape prosecution for the incident. She reportedly became angry when she found Miss Engels in a room at the hotel with her sons Robert Mugabe junior, 25, and Chatunga Mugabe, 21.
Miss Engels, who is South African, claimed Mrs. Mugabe's bodyguards did nothing to stop the attack.
"What is a girl compared to a women beating you and 10+ body guards standing back leaving her to do this s***," she wrote on social media.
"She split my head open in 3 places with an extension cord and used the plug to hit me," claimed Miss Engels, who pointed out that as a model her looks is her livelihood.
Miss Engels contacted the police on August 14, about the incident. On Wednesday, August 16, the South African Ministry of Police published a statement in which they said "the suspect" made arrangements to be interviewed at a police station at 10am on Tuesday, August 15.
"The time scheduled was changed several times. By end of business yesterday she had failed to present herself as arranged," said the statement, which added that Zimbabwean government representatives did come to the police station.
"The suspect's lawyers and government representatives made verbal presentations to SAPS (South African Police Service) investigators that the suspect wished to invoke diplomatic immunity cover," said the police.
The police said the Zimbabwean government had then formally submitted a document invoking diplomatic immunity on behalf of the president's wife.
"The suspect remains in South Africa and has not departed the republic. We are advised her itinerary includes amongst private matters her attendance and participation at the scheduled SADC heads of state/governments summit and bi-lateral diplomatic meetings already underway in Pretoria," they added.
But the statement went on to say that arrangements are taking place with the Zimbabwean High Commission to make sure she is "processed through the legal system," which suggests her diplomatic immunity has not been accepted by the police.
The Police Minister, Mbalula Fikile, has come under intense pressure on social media in South Africa to prosecute Mrs. Mugabe, but his boss, President Zuma, may not want to disrupt the good relations he has with the Zimbabwean leader.
Mr. Mugabe's sons were previously living in Dubai, but moved to South Africa earlier this year after their parents reportedly became concerns about their partying habits.