Three refuse workers had tested positive in total, the City said.
One works as part of the removal teams and the other two are office staff.
Those who had been in close contact with the staff members were required to self-quarantine.
The Mitchells Plain Collections Depot closed on Wednesday and the Woodstock Collections Depot was closed on Monday.
The City warned that refuse collection in both these areas would be delayed over the next few days while offices and vehicles were sanitised, and that the service was only likely to resume next week.
“As a result of the positive cases of Covid-19, the facilities need to remain closed for approximately the next three days until deep cleaning and disinfecting have been completed. This includes disinfecting the facilities and vehicles.”
Residents, who live in the affected areas, were requested to keep their bins on their properties and only bring them out on the next scheduled removal day next week.
Excess refuse that cannot fit in the wheelie bins can be bagged and placed next to the bin for removal.
“Residents are implored not to resort to illegal dumping if collection delays cause refuse to build-up to the point where it cannot fit in the wheelie bins,” the City said.
Meanwhile Council said management was “checking in regularly with staff members who have tested positive” and were communicating with the close contacts of the employees to advise on the way forward in terms of quarantining, screening and testing.
The Western Cape now has nearly 12 000 confirmed infections, which accounted for 62% of the over 18,000 cases in South Africa.
Mitchells Plain had recorded 1,158 infections.