Lesufi tested for the virus on Tuesday and went into self-isolation after two staff members from the department's offices in Johannesburg tested positive for Covid-19.
READ | Lesufi self-isolating after two staff members test positive for Covid-19
Staff are expected to return to the head office on Monday once the process is complete.
READ | 29 Eastern Cape schools close due to positive Covid-19 cases, 48 more have suspected cases
Staff members, who were in contact with those who contracted the virus, have been tested and will follow protocols to prevent the spread of Covid-19.
"Once a staff member tests positive, we also trace their contacts.
The department said that Lesufi and Gauteng MEC of Health Bandile Masuku will on Sunday visit the family of a Grade 7 pupil from Kokosi Primary School in Fochville.