The Herald said the four were arrested after attending a ruling Zanu-PF party rally in the south-western city of Bulawayo where Grace Mugabe was jeered during a speech on Saturday.
Prosecutor Jerry Mutsindikwa told a magistrates 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.
The accused are facing a charge of “undermining the authority of the president”, he said.
The incident angered President 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 move that appeared to open the way for his wife 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 on Thursday granted bail to Martha O’Donovan, a 25-year-old American journalist 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”.