The patient died in the care of the Shrewsbury and Telford Hospital NHS Trust (SaTH) on Wednesday and their death was announced by the NHS on New Year's Eve.
It means 314 people have now died in hospitals in Shropshire after catching coronavirus.
Of these 290 deaths have been at SaTH, 19 at the Shropshire Community Health NHS Trust and five at the Orthopaedic Hospital near Oswestry.
On top of this 188 people have died with Covid-19 in care homes in Shropshire since the pandemic began, with 134 of these in the Shropshire Council area and 54 in the Telford and Wrekin borough.
There have been 140 deaths involving coronavirus in Powys, according to the Office for National Statistics.
Meanwhile the UK-wide death toll reached 73,512 after 964 deaths were announced on New Year's Eve - the second highest total reported on one day since the peak of the first wave.
The highest total reported during the second wave was the 981 deaths announced on Wednesday.
The deaths were announced as the nation prepared to spend New Year's Eve at home.
Shropshire moved from Tier 2 to Tier 3 on Thursday, meaning pubs and restaurants are no longer allowed to open apart from for takeaway and delivery.
The majority of England is now in the toughest Tier 4 restrictions, meaning people must stay at home unless they have a valid reason to leave such as work, shopping, exercise or education.