Summerfield Healthcare is offering tests at its centre in Summerfield Road, near West Park.
Professionals will carry out the tests while patients remain in their cars with results normally available within two working days.
Tests will also be available at Summerfield's clinic in Shrewsbury.
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The UK Government has been widely criticised for its low level of public testing - particularly of NHS workers - compared to many other countries.
The lack of NHS testing has caused particular frustration due to the fact that tests are available privately from clinics such as Summerfield.
Randox Laboratories was offering home testing but has now sold out and has "volunteered a significant element" of its tests to the UK Government. Summerfield is also offering mail order home testing.
The Government has consistently promised to "ramp up testing" - most recently promising 100,000 a day by the end of the month - but so far daily coronavirus testing is still around the 10,000 mark.
Unlike the shortage of ventilators, the low level of testing has been widely put down to a lack of laboratory space and logistical difficulties rather than the number of tests available to the Government.
A public drive-through testing centre was set up in Wolverhampton back on March 11, three days after the first confirmed death at New Cross Hospital. But the site off Showell Road was soon scrapped after the Government decided against mass testing.
WATCH: Drive-through tests in Wolverhampton
See how the public were tested in Wolverhampton, before the NHS drive-through centre was scrapped.
Summerfield says the tests are for anyone who feels they may be suffering from coronavirus and is looking for peace of mind.
Dr Grant Charlesworth-Jones, a GP and medical director at Summerfield Healthcare, said: “People are able to book an appointment over the phone and then drive to the testing stations where they remain in their cars as they are tested by staff in appropriate Personal Protective Equipment.
"Secured samples are then taken to the lab for testing.
“Shrewsbury testing is available in the morning and Wolverhampton testing takes place at lunchtimes.
"This allows time to deliver the samples to the laboratory in the afternoon in order to get the results out as quickly as possible.
Testing in Shrewsbury will be carried out at the clinic based in Charlesworth Court, Hotspur Park, Knights Way, while Wolverhampton testing takes place at Summerfield Road.