The temporary complex will be set up on the Galdeford Car Park.
Shropshire Councillor, Vivienne Parry, said: "I've been speaking with the workmen on the site last week and they hope to have it up and running soon.
"It will be a drive-in facility but people will have to book beforehand to take a test.
"It will really boost the capacity for testing in South Shropshire."
The site was surveyed last week with the erection of the station due to start today.
Councillor Parry said: "Alongside vaccinations, identifying individuals who have been infected is the key to beating this virus.
"Although 3.3 million people have been diagnosed in the UK with Covid many more are known to have caught the disease.
"The more testing we have, the more people we can identify carrying the illness and get them to self-isolate."