The 52-year-old wife of President Robert Mugabe is accused of attacking model Gabriella Engels, 20, on Sunday evening.
The 52-year-old wife of President Robert Mugabe is accused of attacking model Gabriella Engels, 20, on Sunday evening at a Johannesburg hotel where her two sons were staying.
Engels has registered a case with the police alleging assault with intent to do grievous bodily harm, saying she suffered deep cuts to her forehead and the back of her head.
"We know where the suspect is," South Africa's police spokesman Vishnu Naidoo told AFP.
"We are still continuing with the investigations. No warrant of arrest has been issued," he added after some reports suggested Grace Mugabe had hurriedly returned to Harare late Tuesday.
The alleged attack threatened to spark a diplomatic tiff between the two neighbouring countries, which have strong political and economic ties.
Zimbabwean government officials have made no comment on the case.
Grace Mugabe allegedly arrived at the Capital 20 West Hotel with bodyguards and accused Engels of partying with her sons Robert and Chatunga, who are both in their 20s and live in Johannesburg.
Pictures on social media appeared to show Engels bleeding from her head after the alleged assault at the hotel in the upmarket business district of Sandton.
Engels said she had been attacked with an electrical extension cord.
"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," she told the News 24 website.
Zimbabwe's president is expected to fly to South Africa later this week for a regional SADC summit which opens in Pretoria on Saturday.
Grace Mugabe is 41 years younger than her 93-year-old husband and the couple has two sons and a daughter.
She regularly speaks at rallies and is seen as one possible contender to take over from her increasingly frail husband, who has ruled Zimbabwe since independence from British colonial rule in 1980.
Last month she urged him to name his chosen successor, reviving speculation about the race to take over from the world's oldest national leader.
The succession battle is 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, drumming up support for her husband 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.
Grace Mugabe appears to not have diplomatic immunity status as she was not in South Africa on official business.
South African Police Minister Fikile Mbalula told reporters on Tuesday that "in terms of foreign citizens, they must understand they have responsibilities, especially those who hold diplomatic passports."
"We have had to act in the interests of the victim," he said.