A spokesman for the Prison Service said there had been "a number of positive cases" at Stoke Heath near Market Drayton, and that they had taken "precautionary measures" as a result.
It comes as the Hinstock and Hodnet area where the prison is located currently has the highest Covid case rate in the county.
The rate for the area stands at 2,818 cases per 100,000 people in the seven days to January 20, with 219 cases.
The next highest rate in the county is 812, at Harlescott and Sundorne in Shrewsbury.
A Prison Service spokesperson said: “Our priority is to limit the spread of the virus and protect the lives of those who live and work in our prisons.
“We have taken precautionary measures at Stoke Heath, in line with public health guidance, following a number of positive cases and continue to closely monitor the situation.”