Mothiba said police had waited all day on Tuesday for Mugabe to hand herself over‚ but she was a no show.
"They said that they would be coming to plead that she has diplomatic immunity‚ but we were supported by NDPP Adv Shaun Abrahams and his provincial head. She has a penchant for abrasive and thuggish behaviour that is completely inconsistent with the decorum and decency expected of a First Lady", said MDC spokesperson Obert Gutu.
Initially, there was some confusion about whether she was in South Africa after the alleged attack, with some news outlets saying she had slipped out of the country to evade arrest. "We don't know where this issue of assault charges is coming from", said a senior government official, who declined to be named because they were not authorized to speak to the press.
The model said: "When Grace entered, I had no idea who she was". They said the suspect could not be named as she had not yet appeared in court.
Nel said Engels had not received sufficient updates from the police, but that arresting Mugabe, like other suspects, sometimes takes time.
Police said Tuesday's abortive court hearing was created to obtain a statement from Mugabe, along with her version of the events, but that she failed to appear as arranged.
On Wednesday it was reported that Grace Mugabe may already have returned to Zimbabwe, but Mbalula insisted she had not tried to leave the country. That girl obviously was in that hotel room at the invitation of the boys, so who deserves the beating here?
The alleged assault extended into a controversy over Bona Mugabe, Mugabe's daughter, who was studying in Hong Kong.
Engels told the AP she would be willing to face Mugabe in court.
She added: "She just completely lost it". A City University spokesman said Bona Mugabe applied through the normal procedures and the university admitted her based on the common admission guidelines, and she would be afforded no special privileges. "I don't want her to get away with this".