According to the authority, those infected were working in an area of the Civic Centre not open to the public.
Furthermore, the council is “working to ensure the outbreak is contained”.
A Southampton City Council spokesperson said:
“We can confirm that eight staff, who were working in one specific area of the Civic Centre that is not normally open to members of the public, have tested positive for COVID-19. We have been working with NHS Test and Trace and Public Health England to respond and ensure that this outbreak is contained, that staff and service users are protected, and that colleagues are supported.
“We are contacting those individuals who may have been in close contact with a confirmed case and advising them to self-isolate and book a test as needed.
“We have closed a specific area of the Civic Centre, which is not normally open to the public, pending a deep clean. All council services are continuing to operate.
“We would like to remind residents that, in line with government guidance, anyone who has COVID-19 symptoms should self-isolate immediately and book a test online or by calling 119.”