The patient died at the Shrewsbury and Telford NHS Trust (SaTH) on Thursday but their death was announced on Saturday.
It is not known whether they were being treated at Princess Royal Hospital in Telford or Royal Shrewsbury Hospital.
It means 205 people have now died in hospitals in Shropshire after contracting the virus, including 185 patients at SaTH, 15 at the Shropshire Community Health NHS Trust and five at the Orthopaedic Hospital in Gobowen.
Sixteen of the 205 deaths have happened since September 27, with no hospital deaths recorded in Shropshire between July 12 and September 26.
Meanwhile at least 163 people with Covid-19 have died in county care homes since the pandemic began, with 113 of these deaths in the Shropshire Council area and 50 in Telford and Wrekin.
However care home deaths have only been recorded since April 10 meaning the true total is likely to be higher.
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Over in Powys, a total of 96 people have died after contracting coronavirus according to the Office for National Statistics, although only 17 deaths have been confirmed by the county's health board.
The NHS announced 208 more coronavirus deaths in England on Saturday, with the patients aged between 26 and 101.
The youngest person to die who did not have a known underlying health condition was aged 47.
The UK-wide death toll, which includes deaths in and out of hospitals within 28 days of a positive test, increased by 326 to 46,555 on Saturday while the country also recorded its one millionth case.
The updated death toll was confirmed ahead of Boris Johnson's press conference, where he announced that a month-long lockdown for England will start on Thursday.