So far, 25 people have tested positive for the virus after an outbreak at Long Lane traveller's camp. In total, 47 people have been tested.
The flare-up has sparked concern, but Craven Arms councillor David Evans insisted people could still visit as long as they follow government guidelines.
He said: “Craven Arms is still open for business and we want both residents and visitors to enjoy everything our wonderful town has to offer. Our Shropshire Hills are part of an area of outstanding natural beauty and everyone who visits our community will be guaranteed a warm welcome.
“We all have a vital role in preventing the spread of coronavirus by always sticking to social distancing guidelines - that’s staying two metres away from others and washing hands regularly.
“I am pleased that drop-in testing sessions are being offered to residents. As well as making it easier for people to get a test, it will also help Shropshire Council and Public Health England gain further insight into the local situation."
A drive-thru testing centre has been in action at Craven Arms Business Park since the weekend, and will continue to operate throughout next week.
All residents in the town can get themselves a test, regardless of whether they have symptoms. It is open from 10.30am to 3.30pm and people can book a test via NHS Test and Trace online or by calling 119. There is also drop-in testing at Halo Community Centre from 10.30am to 1.30pm. No prior booking is required.
Councillor Lee Chapman, chairman of Shropshire’s Health and Wellbeing Board added: “I cannot praise the local community enough for the understanding and support they have shown during this outbreak. The risk to the Craven Arms community is still very low and at this stage in the pandemic, we still expect to see more outbreaks as the virus continues to circulate within communities both locally and across the West Midlands, as well as nationally
“I would like to remind everybody that it is important to wash your hands, maintain social distancing and to wear a face covering to help protect others."