It is not clear where they were heading but they have not been seen on the streets of Harare.
One of the vehicles had broken down on the side of the road, according to BBC correspondents in Zimbabwe’s capital, Harare.
Earlier, leader of the Zanu-PF youth wing, Kudzai Chipanga, said his members would not allow the armed forces to subvert the constitution and were prepared to die to defend President Mugabe.
He told a press conference in Harare that the military chief did not enjoy the support of the “entire defence force”.
Last week, Mr Mugabe sacked Vice-President Emmerson Mnangagwa – his comrade from the 1970s war for independence – and Zanu-PF expelled him after accusing him of disloyalty.
His expulsion was seen as an attempt to pave the way for Mrs Mugabe to be elected vice-president at the Zanu-PF conference next month, putting her in pole position to succeed her 93-year-old husband when he retires or dies.
NewZimbabwe.com quoted a spokesman for the smaller People’s Democratic Party (PDP), Jackson Mafume, as saying General Chiwenga was complcit in allowing the biblical “Delilah [Mrs Mugabe] to capture their Samson [Mr Mugabe].”
Zimbabwe’s state-linked media observed a black-out of yesterday’s press conference by army chief General Constantino Chiwenga, warning that the military will step in if the ruling Zanu-PF party continues with its “treacherous shenanigans” and purges the party of critics of President Robert Mugabe and his wife Grace.
The Zimbabwe Broadcasting Corporation did not cover the press conference while The Herald newspaper took down an article it had initially posted on its website.