The home, in Dorrington, near Shrewsbury, caters for adults with learning disabilities and complex needs, and is run by Consensus Support Services.
A joint statement on the outbreak said the positive tests involved both staff and residents.
It added that everyone who has tested positive has been asked to self-isolate for 10 days.
Residents affected have been asked self-isolate in their accommodation and are continuing to receive support from Consensus.
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Shropshire Council said it was working with Public Health England to "ensure plans are in place to help prevent the spread of Coronavirus".
The authority said the number of positive tests represent 15 per cent of the people living and working in the home.
A statement from the council said: "We understand Consensus have followed government advice and guidelines; it was quick to put measures in place and undertake all necessary health and safety measures to help prevent further transmission of the virus. We continue to work with everyone involved to provide health protection advice and guidance.
A spokesperson for Consensus Services Limited said: “The health and wellbeing of the people we support, and our colleagues is our absolute priority, and we have been doing everything we can to keep them well during this challenging time.
“We have put in place a number of measures to safeguard the people we support, and we would like to thank our colleagues who are working around-the-clock to provide the highest quality care.
“We continue to work alongside relevant authorities who have provided us with testing for everyone in the service, which has undeniably helped us to effectively put in place appropriate care measures.”
Rachel Robinson, Shropshire’s Director of Public Health said: “Local outbreaks such as this are not unexpected during a pandemic and we have seen cases across the county. Our priority is to stop the spread of infection and protect the health and wellbeing of all residents in our community.
“Shropshire Council, along with Public Health England have responded quickly to the outbreak and we continue to support all those that have been affected. The risk to the wider public is low but we are asking everyone to stay alert to help keep themselves and others safe.”