According to the Presidency, Nxesi was admitted to hospital on Monday night.
Nxesi received his test results on Friday and had been in self-isolation.
His admission to hospital comes following the advice of his medical doctors.
Minister Nxesi is the second member of Cabinet to be admitted to hospital after Minerals Resources and Energy Minister Gwede Mantashe.
“We wish both Minister Nxesi and Minister Mantashe well and a speedy recovery,” said Minister in the Presidency Jackson Mthembu.