NHS England said that the patient had died in the care of Shrewsbury & Telford Hospitals NHS Trust (SaTH).
It brings the total number of Covid related hospital deaths in the county to 263.
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Of those, 243 patients died at SaTH, 15 at Shropshire Community Health Trust and five at The Robert Jones and Agnes Hunt Orthopaedic Hospital near Oswestry.
Office for National Statistics (ONS) data also shows 179 people have now died with the virus in county care homes – 127 in Shropshire and 52 in Telford & Wrekin.
ONS figures also show 105 people are suspected to have died with the virus in Powys.