Zimbabwe's first lady Grace Mugabe was under investigation by South African police Tuesday after she allegedly used an extension cord to assault a model in a Johannesburg hotel. The alleged attack threatened to spark a major diplomatic incident between the two countries, which have strong political and economic ties. The 52-year-old wife of President Robert Mugabe is accused of beating Gabriella Engels, 20, on Sunday evening at the hotel where her two sons were staying, leaving the victim with injuries to her forehead and the back of her head. "She hasn't handed herself over yet. We do not know her whereabouts at this stage," police spokesman Vishnu Naidoo told AFP. South Africa's main opposition party, the Democratic Alliance, said Mugabe had returned hurriedly to Zimbabwe late Tuesday, without citing its source. Mugabe allegedly arrived at the hotel with bodyguards and accused Engels of partying with her sons Robert and Chatunga, who are both in their 20s and live in Johannesburg. South African Police Minister Fikile Mbalula had earlier said Mugabe had turned herself in to officers, but Naidoo said this "just didn't materialise as it was supposed to". "As long as we don't have a suspect in custody, we cannot say when they will appear in court," he added. Pictures on social media appeared to show Engels bleeding from her head after the alleged assault at the Capital 20 West Hotel, in the upmarket Johannesburg district of Sandton. "We were chilling in a hotel room, and (Mugabe's sons) were in the room next door. She came in and started hitting us," Engels told the Times Live website. "The front of my forehead is busted open. I'm a model and I make my money based on my looks." Police Minister 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. We have had to act in the interests of the victim." - A future president? - On Monday, Engels registered a case with the police alleging assault with intent to do grievous bodily harm. Sizakele Nkosi-Malobane, a provincial minister in South Africa's Gauteng province, told Jacaranda FM radio that the case must be pursued fully 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 is 41 years younger than her 93-year-old husband and has two sons and a daughter with the Zimbabwean president. She regularly speaks at rallies in Zimbabwe and is seen as one possible contender to take over from her increasingly frail husband. Last month she urged her husband to name his chosen successor, reviving speculation about the race to take over from the world's oldest national leader. President Mugabe has ruled Zimbabwe since independence from British colonial rule in 1980. The succession battle is widely 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, speaking regularly at meetings to drum 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. The Zimbabwe government has so far made no comment on Grace Mugabe's case.