The global aviation industry is battling to survive a plunge in demand caused by the virus, with some airlines seeking government bailouts or grounding most of their fleets.
SA Express, which flies to domestic and regional destinations, said it would accommodate customers on alternative flights and non-critical staff would go on compulsory leave.
"The airline will utilise this period to review its current network and streamline operations for improved efficiency," it said in a statement.
SA Express entered a form of bankruptcy protection this year, after a court battle with a contractor, logistics firm Ziegler.
It is a separate business from much larger state carrier South African Airways, which is also under bankruptcy protection. (Reporting by Alexander Winning; Editing by Shri Navaratnam and Clarence Fernandez)

Without the urgent funding from the Department of Public Enterprises which oversees the operations of SA Express, the state-owned airline might struggle to pay salaries beyond February 2020 to its about 1,000 employees and business rescue proceedings might be hobbled. (Photo: EPA / Mikko Pihavaara)