The Vesnova orphanage in the central Hlusk district is home to 174 children and young adults with severe disabilities and weak immune systems.
Ten staff members and 13 children were infected as of Thursday.
The orphanage has appealed to the Belarusian government to relocate the sick to hotels and other accommodation.
The Vesnova orphanage is financially supported by Irish charity Chernobyl Children International. It largely cares for abandoned children, and those whose parents are too impoverished to support them.