The party says that in 2019 there were 1241 attendances at A&E at the Royal Shrewsbury Hospital as a result of crashes on the county's roads.
It says cutting the speed limits would reduce demand on A&E and free up beds, ICU services and medical staff time for covid-19.
The Green party has asked the UK minister for roads, Baroness Vere of Norbiton, to introduce the 20mph policy nationally with immediate effect as a response to the virus emergency and to run for as long as that emergency exists.
Hilary Wendt, co-ordinator of the South Shropshire Green Party, said the country had done this once before - in December 1973 - in response to the oil crisis emergency.
"Shropshire Council has all the necessary legal powers to reset all roads currently designated as 30mph to 20mph. We have asked Shropshire Council to take this initiative now to free up capacity in the Royal Shrewsbury Hospital to release beds and medical staff time to deal with covid-19 patients and all non-covid-19 serious health issues," she said.
“We are very concerned indeed about the huge pressures on NHS staff and hospitals beds at a time of extreme emergency caused by the covid-19 virus.
"It is essential to reduce those pressure in any way possible so we can deal more effectively with covid-19 patients and at the same time protect capacity to deal with serious health issues such as strokes, heart attacks and cancer screening and treatment.
"We can do this by lowering speed limits and we need to act quickly. We lowered speed limits in 1973 in response to the oil crisis and the virus crisis is much more serious than that.”