The Robert Jones and Agnes Hunt Orthopaedic Hospital, near Oswestry, will be closed to all visitors except those wanting to visit any patients receiving end-of-life care.
Hospital bosses say any other relatives who feel they have exceptional circumstances as to why they should be allowed to visit will need to discuss on a case-by-case basis with the nurse in charge.
Exceptional circumstances could refer to people with a learning disability or dementia, where there may be increased distress.
It could also mean that allowing a visitor may be of significant benefit to that patient.
Community hospitals run by Shropshire Community Health in Bridgnorth, Ludlow and Whitchurch are also closed to all visitors except those wanting to visit any patients on an end-of-life care pathway or those on a dementia care plan.
Hospital chiefs say they have made the decision to protect patients and staff, recognising the growing prevalence of Covid-19 in the community and concern that the spread of the Omicron variant could put unsustainable pressure on services over the next few weeks.
Those who are able to visit patients under exceptional circumstances should not visit if they are experiencing symptoms, or if they have been in contact with someone who is a suspected or confirmed case of Covid-19 in the past 14 days.
Visitors must also wear a surgical face mask provided by the trust on arrival, and must follow guidance on hand hygiene and social distancing.
The majority of visiting has also been banned at Shrewsbury and Telford hospitals since the beginning of the Covid pandemic.