Mr Machar said he showed no symptoms but would self-isolate for 14 days.
This was contained in a statement posted on Monday on the office's Facebook page and attributed to press secretary James Gatdek Dak.
Machar “has issued a public statement declaring that he is found positive, and from today will self-quarantine in his residence for the next 14 days.”
The Vice-President’s wife, Defence Minister Angelina Teny, some bodyguards, and other staff have also tested positive.
He was tested on May 13, 2020. This was after one of the members of the government task force leading the fight against COVID-19 tested positive.
The Vice -President was a member of the task force until last week.
According to the latest figures from the health ministry, also released on Monday, South Sudan, which is now emerging from a six-year civil war, has so far recorded 339 cases of COVID-19 and 6 deaths.
Though the number is relatively low, aid agencies have said there could be a sharp rise in recorded cases in coming days
Last week, the UN said at least two people living in camps for the internally displaced had tested positive raising fears that coronavirus could spread rapidly in the overcrowded camps.