The patient died in the care of the Shrewsbury and Telford Hospital NHS Trust (SaTH) on Thursday and their death was announced on Saturday.
It was the first Covid-19 death in a hospital in Shropshire for 13 days, according to the latest NHS data. No further deaths were announced on Sunday.
It means 185 people have now died in the county's hospitals after contracting the virus, with 166 of these deaths at SaTH, 14 at the Shropshire Community Health NHS Trust and five at the Orthopaedic Hospital near Oswestry.
A further 139 people have died with Covid-19 in care homes in the county according to the Office for National Statistics, with 95 of these in the Shropshire Council area and 44 in Telford & Wrekin.
However care home deaths have only been recorded since April 10 meaning the death toll is likely to be higher as the first hospital death in Shropshire happened on March 15.
The UK-wide death toll released by the Government, which includes deaths in and out of hospitals, increased by 22 to 44,220 on Sunday.
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The number of deaths in English hospitals increased by 39 on Saturday and then by a further 18 on Sunday to a total of 28,889.
The death toll in Wales increased by six over the weekend to a total of 1,531 but no new deaths were announced in Powys where the ONS says 92 people have died with coronavirus since the pandemic began.
Meanwhile pubs, hairdressers and attractions across the country have reopened as lockdown restrictions were eased.