Michael Makuei told BBC that all the former members of the high-level task force on coronavirus, except the health minister, have tested positive for Covid-19.
He, however, denied reports that President Salva Kiir - who was also a member of the team - had also tested positive.
This is coming days after first Vice-President Riek Machar announced he had tested positive alongside his wife, Defence Minister Angelina Teny.
They tested positive after coming into contact with a former member of the team, who has Covid-19.
The minister said that all the ministers who have tested positive, are now in self-isolation and are in good health.
A number of the bodyguards and staff of the officials also tested positive and are quarantined.
South Sudan has seen a sharp increase in coronavirus cases in recent days with 481 confirmed cases and six deaths.
Experts have raised concerns that the poor healthcare system in South Sudan could cause havoc.
The poor healthcare system is due to the many years of conflict, while hundreds of thousands are living in camps for displaced people.