Zimbabwe has blocked flights by South Africa's government-owned airline amid tensions over allegations that Zimbabwe's first lady assaulted a young model.
South Africa's government said it had not yet decided to grant the Zimbabwe government's request for diplomatic immunity for Grace Mugabe.
She has not commented on the allegations.
Local media reported that Mrs Mugabe was expected to attend a regional summit with 93-year-old President Robert Mugabe in South Africa's capital, Pretoria.
It would be her first public appearance since the alleged assault in a luxury Johannesburg hotel on Sunday night.
Gabriella Engels, 20, has claimed that Mrs Mugabe whipped her with an extension cord, cutting her forehead.
Her lawyers have threatened to go to court if immunity is granted.
Foreign ministry spokesman Nelson Kgwete said South Africa was still considering the request. "Decision yet to be made," he said in a text message.
South African police have issued a "red alert" at borders to ensure Mrs Mugabe does not leave undetected.
Police also say their investigation is complete but needs a government decision on the immunity appeal.
South African Airways said Zimbabwe had placed restrictions on its operations, affecting its flights between the neighbouring countries.
It said its flight from Zimbabwe's capital to Johannesburg was unable to take off as scheduled on Saturday morning. Another flight from Johannesburg to Harare has been cancelled.
South African Airways said Zimbabwean authorities were demanding a "foreign operators permit".
It said it has been flying to and from Zimbabwe for more than 20 years and the permit was never required until Saturday morning.
Civil Aviation Authority of Zimbabwe chief executive David Chawota did not specify the "issues" requiring attention. "The South Africans know what should be done in terms of processes," he said.
The scandal over Mrs Mugabe is a sensitive issue for South Africa as it weighs the possible diplomatic fallout from Zimbabwe if it acts against the first lady and the likely outrage at home if it grants immunity and allows her to leave.
Some demonstrators protested on Saturday in Pretoria against Mr Mugabe and his wife, saying she should be prosecuted.
It is not clear whether Mrs Mugabe entered South Africa on a personal or diplomatic passport. Zimbabwe's state-owned newspaper reported last weekend that she was in South Africa for medical care.
But she told police after the alleged assault that she was scheduled to attend the summit with her husband.