Nisa Local, next to the A458 in Much Wenlock, has confirmed five positive tests, and said it was working with local health officials over the issue.
Shropshire Council said a number of measures had been taken by the supermarket after the five members of staff were required to self isolate for 10 days.
Another member of staff who had been in close contact with those affected is also isolating according to the authority.
The shop is still open but a deep clean of the store is taking place over the weekend.
John Corbo, who owns the supermarket, said in a statement the shop would be cleaned on Saturday but a post on its Facebook page says it will be cleaned on Sunday.
It comes as the council confirmed that the number of positive tests in an outbreak at Rea Valley Speciality Foods in Minsterley had risen from nine to 14.
The Government is currently considering implementing a new national lockdown for England from as early as next week as infection rates rise across the country.
Rachel Robinson, Shropshire Council’s director of public health, said: “We want to reassure residents in Much Wenlock that the risk of infection is very low.
"We are satisfied that the management have taken all the necessary precautions to limit the spread of the virus.
More Covid-19 coverage:
“At this stage in the pandemic we expect outbreaks, as the virus continues to circulate within communities locally and nationally. So far, we have no further evidence of any community transmissions.
“Protecting the health of our population remains a priority, and at this time we would also like to remind everyone to follow social distancing advice to reduce their social interaction with other people."
Latest Covid-19 infection rates in the region
The latest rolling seven-day infection rate of Covid-19 by local authority area, compared to the previous week.
The figures are for the seven days to October 26, with data for the most recent four days (October 27-30) excluded as it is incomplete and does not reflect the true number of cases.
The rate is expressed as the number of new cases per 100,000 people.
From left to right, it reads: name of local authority; rate of new cases in the seven days to October 26; number (in brackets) of new cases recorded in the seven days to October 26; rate of new cases in the seven days to October 19; number (in brackets) of new cases recorded in the seven days to October 19.
South Staffordshire 401.1 (451), 237.5 (267)
Cannock Chase 343.4 (346), 230.2 (232)
Walsall 336.3 (960), 235.0 (671)
Sandwell 317.9 (1044), 223.5 (734)
Stoke-on-Trent 315.9 (810), 221.6 (568)
Birmingham 276.4 (3156), 240.6 (2747)
Dudley 260.6 (838), 163.9 (527)
Wolverhampton 251.0 (661), 197.8 (521)
Stafford 243.3 (334), 162.4 (223)
Lichfield 234.8 (246), 164.2 (172)
Solihull 229.2 (496), 225.5 (488)
Telford and Wrekin 219.6 (395), 168.5 (303)
Shropshire 135.5 (438), 87.3 (282)
Mr Corbo said: "The safety of both our staff and customers is of paramount importance. We are confident that our facilities have solid safety measures in place and that our staff are acting responsibly.
"We have worked extremely hard to make our store Covid-19-secure to keep everyone safe. A deep clean of the store is taking place on Saturday.
“We want to reassure members of the local community that we are doing everything possible to control any spread of the virus.
“We continue to work closely with Shropshire Council, and we will continue to support the staff members who have been affected.
“I would also like to thank our loyal customers for their continued support during the pandemic.
Numerous businesses across Shropshire have been affected by outbreaks in recent days, while Telford is being moved from Tier 1 to Tier 2 of the coronavirus restrictions on Saturday after a spike in cases.
Mrs Robinson added: "Good hand hygiene remains the best protection against the virus, including washing your hands more regularly with soap and water for at least 20 seconds, and covering your mouth and nose with a tissue when you cough or sneeze.
"If you are showing coronavirus symptoms, or if you or any of your household are self-isolating, for example if you have been contacted by NHS Test and Trace, you should stay at home – this is critical to staying safe and saving lives.”