Both cases are adults who have travelled back to the UK from Italy.
The news was revealed at a meeting of Shropshire's Clinical Commissioning Group (CCG) on Wednesday afternoon.
Sam Tilley, director of planning for the CCG, said the cases are not connected.
The board was also told drive-through testing for coronavirus will be available in Shrewsbury from Thursday - stressing those wishing to be tested must first call 111, rather than simply turning up.
Telford is expected to have a drive-through testing facility by the weekend.
NHS England confirms two more patients have died from coronavirus, taking the total to 10. Both in London and had underlying health problems.
A total of 590 people have tested positive for coronavirus in the UK as of 9am on Thursday, up from 456 at the same point on Wednesday.
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Global infections are now over 126,000.
147 people had been tested for coronavirus in Shropshire as of Tuesday
One patient has died in Wolverhampton and one in Dudley, while four other others in Wolverhampton have tested positive, plus four in Staffordshire and one in Birmingham
Wales confirmed a further nine positive diagnoses on Tuesday evening, taking the country’s total to 15, while 10 new cases were confirmed in Ireland
Three Leicester City players have shown symptoms of coronavirus and been placed in self-isolation.
Steve Gregory, executive director of nursing and operations at Shropshire Community Health NHS Trust, said: “The NHS in Shropshire, Telford & Wrekin is establishing a new drive-through service for testing people who may have coronavirus. This will be provided in Shrewsbury and Telford.
“People will only drive to a testing facility if they have been given an appointment, following a telephone assessment by NHS 111. It is NOT a drop-in centre and ONLY those who meet the nationally agreed criteria for a suspected case will be asked to attend and given an appointment for their test. Only referred cases will be tested.
“Those referred to the centre for swabbing will arrive in their own car, and will not enter the building. They will be swabbed outside by a specially-trained healthcare professional behind a private screen.
“This service is being provided by clinical staff from Shropshire Community Health NHS Trust. We are doing this to minimise the impact of testing on local hospitals, which is where cases have been tested in recent weeks.
“If you have any concerns about your own health in relation to coronavirus, please follow the national guidance provided by NHSE.
“We are expecting this service to go live in Shrewsbury tomorrow and in Telford by the weekend.”
Rachel Robinson, Shropshire Council’s director of public health, said: "We can confirm a second case of confirmed COVID-19 within Shropshire Council local authority area.
"This is not linked to the first case we confirmed yesterday (Tuesday, March 10).
"As with the first case, this is a case in an adult who had returned from an infected area.
“I’d like to reassure people that the risk to the general public remains low and Shropshire Council is working with health colleagues to do everything we can to stop the virus spreading and ensure the people of Shropshire are protected.
“Public Health England (PHE) are identifying and speaking to those who have been in close contact with the individual, and will follow up with any appropriate action.
"If you have not been contacted by Public Health England as a close contact of either of the two confirmed cases, you do not need to take any further action at this time.
“We have been working, and continue to work, closely with our PHE and NHS partners to do everything we can to help prevent the spread of the virus. However, as we continue to contact trace, we anticipate there may be a further increase in the number of cases.
“Good hygiene is the best prevention and there are some simple steps you can take to protect you and your family by washing your hands regularly and thoroughly, and if you cough, cover your mouth and nose with a tissue.
“If you have recently been to one of the affected areas and are feeling unwell, you should phone the NHS 111 helpline for further advice straight away – please don’t go to your doctor or a hospital.
"There’s lots of advice on how people can protect themselves online at www.nhs.uk/coronavirus.”
Katie Spence, deputy director of health protection for Public Health England, West Midlands, said: "Public Health England is contacting people who had close contact with the latest confirmed cases of COVID-19.
"The case is a resident within Shropshire Council local authority area who became infected whilst travelling in Italy.
"Close contacts will be given health advice about symptoms and emergency contact details to use if they become unwell in the 14 days after contact with the confirmed case. This tried-and-tested method will ensure we are able to minimise any risk to them and the wider public.
“We will not be commenting further on the details of this particular case due to need to protect patient confidentiality.”