Her husband, Zimbabwean President Robert Mugabe, has meanwhile arrived in South Africa for a regional summit, complicating the diplomatic dilemma confronting the government.
Grace Mugabe, 52, has asked for diplomatic immunity in the case, but she has not been charged.
Her whereabouts were not known to the authorities yesterday.
The alleged victim, 20-year-old model Gabriella Engels, has accused Mugabe of barging into a hotel where Engels was meeting with Mugabe’s sons, and whipping her with an electric cord.
Police Minister Fikile Mbalula told reporters on Wednesday that Grace Mugabe had been due to appear in court on Tuesday afternoon under a deal struck with authorities, but failed to turn up.
Yesterday Mbalula said that police had put a “red alert” for the first lady on South Africa’s borders.
“We had already put tabs on the borders, in relation to her leaving the country, so there’s no question about that,” he told reporters.
So far she had made no attempt to flee, he added.
The South African government has made no official comment on the case and foreign ministry spokesmen have not answered their phones for two days, but the issue is causing waves at the highest level.
Justice Minister Michael Masutha told Reuters that he was attending a meeting on Wednesday evening to discuss the matter.
The police have said Grace Mugabe will get no special treatment.
Former state prosecutor Gerrie Nel said the Engels family had been approached by a third party to accept a cash settlement to drop the case.
“The family is not interested in doing that,” said Nel. “They said let us talk and make this go away. No amount was mentioned.”
Nel, who laid out the murder case against track star Oscar Pistorius and is nicknamed “the Pitbull”, told a news conference that he was ready to represent Engels.
He said an investigator had told him police were preparing an arrest warrant for Mrs Mugabe.
However, a senior police source said that was not the case.
“We are not preparing an arrest warrant yet,” the source said. “Our investigations were completed, but before we could take the next step, the suspect applied to invoke diplomatic immunity. We are waiting the outcome before we can move on to the next step.”
Debbie Engels, mother of the alleged victim, said: “Now I know that this woman is not going to get off scot free for what she did.”
A police statement on Wednesday said Grace Mugabe would be “processed through the legal system”.
She had come to South Africa for medical treatment to an injured foot, almost certainly invalidating her claims to diplomatic immunity, legal experts said.
However, given the potential for diplomatic fallout, prosecutors could decide to drop the case if they thought the injuries to the alleged victim were not too severe, criminal attorney Riaan Louw said.
The Harare government has made no official comment and requests for comment from Zimbabwean government officials have gone unanswered.
A lawyer identified to Reuters as Grace Mugabe’s representative declined to answer any questions.
Zimbabwe’s ambassador to Pretoria, Isaac Moyo, did not answer his phone.
President Mugabe, 93, arrived at a military air base near Pretoria late on Wednesday for a regional summit.
Reporting his visit, Zimbabwe’s Herald newspaper, the Harare government’s main mouthpiece, made no mention of the controversy swirling around his wife.
South Africa has a difficult relationship with its northern neighbour.
It is home to an estimated 3mn Zimbabwean exiles who regard Mugabe as a dictator who has ruined their country.
But Mugabe is still seen by many Africans as the continent’s elder statesman and a hero of its anti-colonial struggles.
Previous South African leaders, including Nelson Mandela, whose relationship with Mugabe was forged during the anti-colonial and anti-apartheid struggles, had often deflected Western criticism of him.
Mugabe’s relationship with President Jacob Zuma has been testier, however.
Debbie Engels, the mother of the alleged victim, has released graphic pictures to the media of her daughter’s injuries, showing gashes to her head and bruises on various parts of her body.
“I just want justice for my daughter. It’s not about money. It’s about justice. She attacked my child for no reason,” Engels told Reuters.
Reuters has not been able to verify key aspects of the assault allegations independently.
Debbie Engels has provided details of the incident, relayed by her daughter.
She describes Grace barging into a hotel room where Gabriella and two female friends were waiting to meet one of Mugabe’s two adult sons.
“This woman comes in screaming, calling them names and whatnot and demanding to know where her sons were,” Debbie Engels said. “They kept telling her ‘They’re not here’.”
Gabriella said Mugabe’s security guards followed her into the room, stood by and watched throughout, Engels said.
“She (Grace) had an electric cord wrapped around her hand and she started attacking them. She hit my daughter with a plug socket,” Engels said.
