The building underwent a deep clean on Monday following reports of positive cases, before the venue was closed on Wednesday.
Julia Burrows, director of public health at Barnsley, said: “We’re aware of a six positive confirmed cases of coronavirus at Barnsley’s Royal Mail sorting office, with further cases possible as investigations and staff testing continues.
“A number of staff are self-isolating.
“The building remains closed for deep cleaning before reopening is considered.
“Barnsley Council’s regulatory service team and colleagues from Public Health England are working with Royal Mail to understand how the virus is being spread across the workforce; looking at possibilities inside and outside of the premises and what we can do to reduce and prevent this.
“A number of measures have been implemented to prevent the spread of coronavirus on the site, and these will be reviewed with the company.
“The council is working closely with Royal Mail to provide advice and support and are in the process of reviewing risk assessments.
“Regulatory services officers will be inspecting the premises following the deep clean, once it is back up and running.”
A Royal Mail spokesperson said: “We're sorry to advise that due to resourcing issues, deliveries of mail in the S70, S71, S72 and S75 postcode areas will be limited again today, Friday 26 June.
“As a result, our focus today will be on delivering as many special delivery and tracked items as possible.
“The customer service point will be open during the normal opening hours of 7am - 9am.
“We're sorry but collections from business customers and Post Offices are likely to be affected again today.”