Mrs Mugabe herself and Mr Mnangagwa are the front-runners and their rivalry has split the governing Zanu-PF.
The row comes after Mr Mnangagwa claimed that he was poisoned in August.
His supporters have suggested that rivals within Zanu-PF were responsible, although Mr Mnangagwa has distanced himself from such claims.
He has told state media that he remains loyal to President Mugabe.
An angry Grace Mugabe departed from a prepared speech at an event in Harare to attack Mr Mnangagwa.
"We are being threatened night and day that if a particular person does not become president we will be killed," she said.
"We will not bow to that pressure. They say there will be a coup, but no-one will recognise you. The African Union will not recognise you, the SADC [Southern African Development Community] will not."
Mr Mnangagwa fell ill at a political rally led by President Mugabe in August and had to be airlifted to South Africa for treatment.
His supporters suggested a rival group within Zanu-PF had poisoned him and appeared to blame ice cream from Mrs Mugabe's dairy firm.
But on Thursday, Mrs Mugabe dismissed the suggestions.
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