During the incident, which occurred on Sunday, Mugabe, 52, allegedly attacked Gabriella Engels, 20, with an extension cord.
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.
"We are dealing with the matter and will get the full report," Police Minister Fikile Mbalula told the local Eyewitness News agency.
"If she came here with her diplomatic passport, she'll have diplomatic immunity. This doesn't mean she cannot be arrested."
Pictures on social media appear to show Engels with a bleeding head injury after the alleged incident in Capital 20 West Hotel in the upmarket district of Sandton.
Mugabe allegedly arrived with bodyguards and accused Engels of living with her sons Robert and Chatunga, both in their 20s, who are based in the city.
"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.
"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.
Foreign affairs spokesman Clayson Monyela said Mugabe's trip was "a private visit so government cannot get involved if an alleged crime is committed."
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.
The Zimbabwe government made no immediate comment.