A total of 12 staff have tested positive for Covid-19 at the store since September 29.
Staff who need to self-isolate are continuing to do so, while others who have completed their self-isolation period have now returned to work.
Proactive testing is continuing at the store, in New Square.
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The supermarket says it is working proactively with Sandwell Council and Public Health England (PHE) Midlands to keep their staff and customers safe and prevent the transmission of the virus.
A spokesman for Tesco said: "A number of colleagues at our West Bromwich Extra store have tested positive for Covid-19. Their close contacts have been informed.
“The safety of our colleagues, customers and suppliers remains our number one priority and we are working with local public health authorities, following all Government guidance and taking the relevant precautions.
“We have extensive measures across all of our stores to help keep everyone safe, including protective screens at every checkout, social distancing signage and regular cleaning.”
A Sandwell Council spokesman added: "We are working closely with Tesco West Bromwich and we are carrying out proactive Covid-19 testing with staff members.”