The two deaths announced on Wednesday take the county's hospital Covid-19 death toll to 159, with an additional 112 deaths confirmed in Shropshire care homes.
The official UK Government death toll increased by 412 to 37,460 today although analysis suggests more than 45,000 people have died with Covid-19 across the UK.
The number of patients to have died in English hospitals increased by 183 to 26,049.
Both of the Shropshire patients announced to have died today were in the care of the Shrewsbury and Telford NHS Hospital Trust, meaning 142 people have now died with the virus at the county's two main hospitals.
Five patients have also died at the Orthopaedic Hospital in Gobowen and 12 have died in the care of Shropshire Community Health NHS Trust.
Meanwhile the death toll in Wales increased by 11 to 1,293 today, with 13 deaths in Powys so far confirmed by Public Health Wales.
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However figures from the Office for National Statistics (ONS) show that at least 84 people from Powys have died with suspected or confirmed Covid-19.
The ONS also publishes the data for English care home deaths, which shows that at least 72 people have died with the virus in homes in the Shropshire Council area and 40 have died in homes in the Telford & Wrekin Council area.
These figures are only available for April 10 to May 22 meaning the true total is likely to be far higher.
The daily hospital figures include Covid-19 patients whose deaths were confirmed in the previous 24 hours, not who died in that period.
Some deaths are not included in the statistics for several days due to testing or family members being informed.
The news came as Boris Johnson was set to be questioned by senior MPs as he faces a growing Tory revolt and plummeting poll ratings over the Dominic Cummings row.
Meanwhile, one million UK businesses have claimed £15 billion from the Government’s Coronavirus Job Retention Scheme to cover the wages of 8.4 million staff unable to work during lockdown, new official figures show.
The Treasury also revealed that UK banks have funnelled more than £27 billion to companies as part of three state-backed loan schemes since Covid-19 shut down large parts of the economy.