The patient died in the care of the Shrewsbury and Telford Hospital NHS Trust (SaTH) on Wednesday and their death was announced today.
It means the confirmed Covid-19 death toll in Shropshire is now 315, with 182 of the deaths happening in hospitals.
A total of 163 patients have died with the virus at SaTH along with five at the Orthopaedic Hospital near Oswestry and 14 at the Shropshire Community Health Trust.
An additional 133 people have died with the virus in Shropshire care homes, although figures for care home deaths are only available from April 10 to June 16.
The first Covid-19 death in a Shropshire hospital happened on March 15.
Meanwhile the UK-wide death toll, which includes deaths in and out of hospitals, increased by 173 to 42,461 today.
The number of deaths in English hospitals went up by 46 to 28,221 and in Wales the death toll increased by four to 1,475.
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So far at least 89 people have died with the virus in Powys, according to the Office for National Statistics, although only 14 deaths have been recorded in the county's hospitals.
Today the UK’s chief medical officers agreed to downgrade the coronavirus alert level from four to three after a “steady” and continuing decrease in cases in all four nations.
Localised outbreaks of Covid-19 are still “likely” to occur, the advisers warned, and the virus remains in general circulation.
But the downgrading – recommended by the Joint Biosecurity Centre (JBC) – means transmission of coronavirus is no longer considered to be “high or rising exponentially”.
Health Secretary Matt Hancock said moving to a lower alert level is a “big moment” for the UK, and showed the country is getting “back on her feet”.