During the incident, which occurred on Sunday, Mugabe, 52, allegedly attacked Gabriella Engels, 20, with an extension cord, leaving her with wounds on her forehead and the back of her head.
“She’s not under arrest because she cooperated and handed herself over to the police,” South African Police Minister Fikile Mbalula told reporters.
“In terms of foreign citizens, they must understand they have responsibilities — especially those who hold diplomatic passports.
“I cannot just go to Zimbabwe and beat up people there and then the matter will disappear.
“From the police side, we have had to act in the interests of the victim, we have opened a case.”
Pictures on social media appeared to show Engels with a bleeding head injury after the alleged incident in Capital 20 West Hotel in the upmarket Johannesburg district of Sandton.
Mugabe allegedly arrived with bodyguards and accused Engels of partying with her sons Robert and Chatunga, both in their 20s, who are based in the South African city.
– ‘She started hitting us’ –
“We were chilling in a hotel room, and (the sons) were in the room next door. She came in and started hitting us,” Engels was quoted as saying by the TimesLIVE website on Monday.
“The front of my forehead is busted open. I’m a model and I make my money based on my looks.”
Mugabe, who is 41 years younger than her husband Robert, has two sons and one daughter with the Zimbabwean president.
“There was a criminal case opened in Sandton at Morningside (station) yesterday, but I can not release any name. Right now we have not arrested anybody,” national police spokesman Vish Naidoo told AFP.
Sizakele Nkosi-Malobane, a provincial minister in Gauteng province, told Jacaranda FM that the case should be pursued through the courts.
“We hope that it will send a strong message to all leaders who abuse their power and assault innocent people in our country,” she said.
Grace Mugabe regularly speaks at rallies in Zimbabwe and is seen as one potential successor to take over from her increasingly frail husband.
Last month she urged her 93-year-old husband to name his chosen successor, fuelling renewed speculation about the race to take over from the world’s oldest national leader.
The Zimbabwe government made no immediate comment.