Johannesburg - A court appearance for Zimbabwe First Lady Grace Mugabe, relating to an alleged bloody attack against a model, is not yet on the table, said police spokesperson Vishnu Naidoo.
"As long as we don't have a suspect in custody, we cannot say when they will appear in court."
Police Minister Fikile Mbalula had earlier said that Mugabe had turned herself in to officers.
"The minister learned later that it just didn't materialise as it was supposed to," Naidoo said.
Grace Mugabe, 52, is under investigation after she allegedly used an extension cord to assault 20-year-old Gabriella Engels who was visiting Mugabe's two sons in a Johannesburg hotel on Sunday evening.
No hand over
"She hasn't handed herself over yet. We do not know her whereabouts at this stage," Naidoo told AFP.
Grace Mugabe allegedly arrived at the hotel with bodyguards and accused Engels of partying with her sons Robert and Chatunga, both in their 20s, who live in the South African city.
Read the full story here: I had no idea who she was, says model about Grace Mugabe
Engels registered a case of assault with intent to do grievous bodily harm with the police.
Pictures on social media appeared to show Engels bleeding from her head after the alleged incident at the Capital 20 West Hotel, in the upmarket Johannesburg district of Sandton.
"We were chilling in a hotel room, and (the sons) were in the room next door. She came in and started hitting us," Engels told the Times Live website.
"The front of my forehead is busted open. I'm a model and I make my money based on my looks."
Police Minister Mbalula told reporters "in terms of foreign citizens, they must understand they have responsibilities, especially those who hold diplomatic passports.
"I cannot just go to Zimbabwe and beat up people there and then the matter will disappear. We have had to act in the interests of the victim."
Gauteng Community Safety MEC Sizakele Nkosi Malobane told Jacaranda FM radio that the case should be pursued fully through the courts.
"We hope that it will send a strong message to all leaders who abuse their power and assault innocent people in our country," she said.
Grace Mugabe, who is 41 years younger than her husband Robert, 93, has two sons and one daughter with the Zimbabwean president.
She regularly speaks at rallies in Zimbabwe and is seen as one possible contender to take over from her increasingly frail husband.
Last month she urged her husband to name his chosen successor, reviving speculation about the race to take over from the world's oldest national leader.
President Mugabe has ruled Zimbabwe since independence from British colonial rule in 1980.
Who is Grace backing?
The succession battle is widely expected to pit Vice President Emmerson Mnangagwa against a group called "Generation 40" or "G40" because its members are generally younger, and which reportedly has Grace's backing.
While Grace Mugabe has in the past denied harbouring ambitions to take over from her husband, at other times she has said she would be prepared to serve in any political position.
She has taken on a larger public role in recent years, speaking regularly at meetings to drum up support for the president and heading the women's league of the ruling Zanu-PF party.
In speeches this year the president has often slurred his words, mumbled and paused for lengthy periods.
His reign has been marked by brutal repression of dissent, mass emigration, vote-rigging and a sharp economic decline since land reforms in 2000.
The Zimbabwe government has so far made no comment on Grace Mugabe's case.