The 52-year-old wife of President Robert Mugabe is accused of attacking Gabriella Engels with an electrical extension cord on Sunday evening at a Johannesburg hotel where the first lady's two sons were staying.
Engels has registered a police case alleging assault with intent to do grievous bodily harm, saying she suffered deep cuts to her forehead and the back of her head.
"The suspect('s) lawyers and her government representatives made verbal representations... That the suspect wished to invoke diplomatic immunity cover," the police ministry said in a statement.
They added that she would attend at the weekend a summit of the Southern African Development Community (SADC) in Pretoria where her husband and other heads of state will be present.
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Her official duties at the summit could bolster her claim to diplomatic immunity, after her trip to see her sons was widely described as private.
Foreign affairs spokesman Clayson Monyela had told AFP yesterday that her trip was "a private visit so government cannot get involved."
"We are still continuing with the investigations. No warrant of arrest has been issued," he added, after some reports suggested she had hurriedly returned to Harare late yesterday.
The alleged attack threatens to spark a diplomatic tiff between the two neighbouring countries, which have strong political and economic ties.
Zimbabwean 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.
Engels said she was 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.
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 a possible contender to take over from her increasingly frail husband, who has ruled Zimbabwe since independence from British colonial rule in 1980.
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.