The Herald said the four were arrested after attending a ruling ZANU-PF party rally in the country's southwestern city of Bulawayo where Grace Mugabe was jeered during a speech on Saturday.
Prosecutor Jerry Mutsindikwa told a magistrate court that "the quartet, with others allegedly sang the song 'into oyenzayo siyayizonda'" -- whose lyrics in Ndebele mean "we hate what you are doing" -- while Grace addressed the rally.
They are "facing a charge of undermining the authority of the president," he said.
The incident angered Mugabe who spoke at the same rally shortly after his wife, accusing his deputy Emmerson Mnangagwa of organising and sponsoring the hecklers.
He vowed to fire Mnangagwa, which he did two days later, in a dramatic move that appeared to open the way for his wife Grace to succeed him in office.
Grace Mugabe could be appointed as one of the country's two vice presidents at the party congress next month.
Mnangagwa who had been touted as an obvious successor to Mugabe, fled into exile this week. His whereabouts are unknown.
The arrest of the four ZANU-PF activists came as the Zimbabwe high court Thursday granted bail to Martha O'Donovan, a 25-year-old American journalist charged with charged with insulting Mugabe and attempting to subvert the regime on account of an alleged tweet that described the ageing leader as "selfish and sick".
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