South African police have issued a "red alert" at the country's borders for Zimbabwe's First Lady Grace Mugabe, the police minister has said.
She is accused of hitting a 20-year-old woman over the head with an extension cord in a hotel room near Johannesburg.
Police expected Mrs Mugabe, 52, to turn herself in on Tuesday, but she failed to show up.
The first lady's whereabouts are not known but she is believed to still be in South Africa.
Zimbabwean President Robert Mugabe is now also in the country ahead of a southern African heads of state meeting due to start on Friday.
Mrs Mugabe has not commented on the allegation.
Police Minister Fikile Mbalula said: "We, in terms of South African police, [have] already put tabs on the borders in relation to her leaving the country, so there is no question about that.
"So tabs have been put, a red alert has been put, so she is not somebody who has been running away."
On Wednesday, South Africa's police ministry said Zimbabwe's government had sought diplomatic immunity for Mrs Mugabe.
Meanwhile, South African lawyer Gerrie Nel, who successfully prosecuted Paralympic athlete Oscar Pistorius, is supporting the woman making the allegation, Gabriella Engels.
Mr Nel is now working with the Afriforum group, which mainly lobbies for the rights of Afrikaners in South Africa.
Afriforum said if the police failed to act in the case then it would take up a private prosecution.
It also said that it would fight any move to grant Mrs Mugabe diplomatic immunity.
Ms Engels told the BBC that she was attacked by Mrs Mugabe who believed she knew the whereabouts of her son, Bellarmine.
"We kept telling her 'we do not know where he is... we haven't seen him for the night'... She cornered me… and started beating the hell out of me.
"That's when she hit me with the plug and the extension cord. And I just remember being curled down on the floor with blood rushing down my face and down my neck.
"She hit us with so much hate."
Ms Engels has now laid an assault charge and added that she wants Grace Mugabe to "go to jail".
Zimbabwean First Lady Grace Mugabe has returned home from South Africa after failing to turn herself in to police in Johannesburg to face accusations of assault, officials say.
It was not immediately clear why Mrs Mugabe did not report to police after saying she would do.
A 20-year-old South African woman has accused Mrs Mugabe of hitting her over the head with an extension cord during a row at a hotel on Sunday evening.
Mrs Mugabe has so far not commented.
Zimbabwean government sources confirmed that Mrs Mugabe, wife of President Robert Mugabe, had returned home.
"Yes, she is back in the country. We don't know where this issue of assault charges is coming from," said one senior official quoted by Reuters.
Earlier, South African police said they had been negotiating with Mrs Mugabe's lawyers to get her to hand herself in.
Confusion surrounded the case with officials saying at one point that Mrs Mugabe had handed herself over to police and would appear in court. She did not appear and police sources later said she had agreed to turn herself in but failed to do so.
Gabriella Engels, a model, accused Mrs Mugabe, 52, of hitting her after finding her with her two sons in a hotel room in Sandton, a wealthy suburb north of Johannesburg.
Ms Engels released an image of a head injury online.
"When Grace entered I had no idea who she was," she told South African broadcaster News24.
"She walked in with an extension cord and just started beating me with it. She flipped and just kept beating me with the plug. Over and over. I had no idea what was going on. I was surprised. I needed to crawl out of the room before I could run away.
"There was blood everywhere," she added. "Over my arms, in my hair, everywhere."
She registered a "case of assault with intent to do grievous bodily harm", police said.
Zimbabwe's first lady, Grace Mugabe, is due in court in South Africa following allegations of an assault, South Africa's police minister says.
She has "handed herself over to the police" but is not under arrest, Fikile Mbalula said.
South African model Gabriella Engels, 20, has accused Mrs Mugabe of hitting her on the head with an extension cord during a confrontation at a hotel.
She released an image of a face injury online. Mrs Mugabe has not commented.
Ms Engels accused Mrs Mugabe, 52, of hitting her after finding her with her two sons in a hotel room in Sandton, a plush suburb north of Johannesburg, the BBC's Pumza Fihlani reports.
The attack is said to have happened on Sunday evening.
In a phone interview for South Africa’s News24 news site, she said: "When Grace entered I had no idea who she was. She walked in with an extension cord and just started beating me with it.
"She flipped and just kept beating me with the plug. Over and over. I had no idea what was going on. I was surprised… I needed to crawl out of the room before I could run away.
"Her ten bodyguards just stood there watching, no-one did anything, no-one tried to help me."
"There was blood everywhere," she added. "Over my arms, in my hair, everywhere."
In a statement, they confirmed that on Monday an unnamed 20-year-old South African woman had registered a "case of assault with intent to do grievous bodily harm".
She was "allegedly assaulted by a prominent woman at a hotel in Sandton," they said, without naming Mrs Mugabe.
Who is Grace Mugabe?
Zimbabwe is to build a $1bn (£770m) university dedicated to the man accused of leading his country to the brink of economic collapse, Robert Mugabe.
Jonathan Moyo, minister of tertiary education, told reporters it was a fitting tribute to the 93-year-old president's "commitment to education and his exemplary leadership".
It is unclear where the money will come from in a country where unemployment and poverty is endemic.
Economic output has halved since 2000.
Last year, more than four million Zimbabweans were in need of food aid due to drought. The country was once known as the breadbasket of southern Africa.
Despite this, the cabinet has agreed to spend $800m building the new university in Mazowe, 35km (20 miles) outside the capital Harare.
Another $200m has been set aside for an endowment fund for research and innovation at the Robert Gabriel Mugabe University, which will focus on science and technology, Mr Moyo said.
He would not be drawn on where the funds were coming from.
The announcement of the new university was met with derision from opposition parties, which hope to end Mr Mugabe's 37-year reign at next year's general elections.
"This is populism that defies logic," said Obert Gutu, a spokesman for the Movement for Democratic Change (MDC). "It is meant to stroke Mugabe's ego because we know this government is broke."
Zimbabwe already struggles to pay for education - as well as public services and infrastructure like roads and hospitals - spending 90% of the country's annual budget on wages.
The MDC says the money would be better spent on Zimbabwe's existing universities, where students face crumbling infrastructure and a lack of accommodation.
According to state media, Mr Mugabe has seven earned degrees and 11 honorary degrees.
He is a trained teacher and after coming to power in 1980, his government massively increased the provision of state education to the previously disadvantaged black majority.
Zimbabwe recently had the highest literacy rate in Africa, at 90% of the population.
Mr Mugabe's wife Grace was awarded a controversial PhD from the University of Zimbabwe in 2014.
Zimbabwe has removed an artificial pitch that was donated by Fifa in 2008 ahead of the 2010 World Cup.
As South Africa hosted the tournament, every nation on the continent received an artificial surface as part of Fifa's Win In Africa With Africa project.
There were questions as to whether the surface at Harare's Rufaro Stadium was good enough for top-flight football.
"A lot of players complained about the hard pitch," said Lloyd Mutasa coach of local side Dynamos.
"Getting back to the natural turf is good for the players."
The surface was not maintained properly and became worn out, and is believed to have been responsible for numerous injuries, particularly knee problems.
After months of work the stadium has re-opened with a natural grass surface, with the country's most popular club Dynamos winning on the opening weekend of action.
Fifa believed that African countries would benefit greatly from the project as an artificial surface can be used as many times a day as wanted, and that it would help countries that struggled to maintain their pitches in very hot or very wet conditions.
But the quality of the donated pitches was not comparable to that of the artificial surfaces that are used in Europe even for training pitches.
So the much-vaunted project that saw then Fifa president Sepp Blatter inaugurate the Rufaro Stadium pitch will be considered a failure from Zimbabwe's point of view.