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".
One option being mentioned in the South African media is that Mrs Mugabe should plead guilty during a short court appearance, and pay a fine.