The person died last Wednesday but their death was only confirmed in weekly figures released by the Office for National Statistics today.
Until last week there had not been a coronavirus death in any of the county's care homes since July 1.
It takes the Covid-19 death toll in care homes in the Shropshire Council area to 106, with a further 50 people having died in homes in the Telford & Wrekin borough.
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A further 189 people have died in the county's hospitals after catching Covid-19 but the most recent of these deaths happened on July 12.
Six more coronavirus deaths were announced in the Midlands today, with four of these in Birmingham and one in Dudley.
Across England 28 more people were confirmed to have died after testing positive for Covid-19, bringing the total number of reported deaths in English hospitals to 29,785.
However some of these patients died more than 28 days after testing positive for coronavirus, meaning they will not be included in the Government's UK-wide death toll which increased by 37 to 41,825 today.
It comes as tighter restrictions are set to come into place in an attempt to curb the rising number of coronavirus cases in the UK.
Boris Johnson warned the UK was at a “perilous turning point” in the battle with coronavirus as he abandoned efforts to get more workers back into offices, ordered wider use of face masks and imposed a 10pm curfew on pubs and restaurants.