Everybody living in Nuneaton and Bedworth will be offered a PCR test after positive cases of the Indian Covid variant were found.
Warwickshire County Council said the cases of the strain known as VOC-21APR-02 were in the Abbey Ward area.
It is stepping up its testing programme, including opening up a second seven-day testing site.
Public health officials said the situation was "manageable" and called for locals to take preventative action.
"It is important to remember that the number of cases of Covid-19 is still very low, and Warwickshire has, as it has throughout the pandemic, acted swiftly and decisively," said Dr Shade Agboola, Warwickshire's director of public health.
"However, as we continue along the roadmap out of lockdown, we need to remain vigilant, and the presence of these cases of the variant of concern clearly demonstrates that need."
The positive cases in the borough were first announced on Thursday. It is thought the Indian variant is more transmissible but the vaccine should still protect against the disease.
On Tuesday, the World Health Organization classified the Indian variant as a "variant of global concern".
Warwickshire County Council announced it was also planning to deliver PCR (polymerase chain reaction) testing kits to large businesses and schools and would be carrying out door-to-door testing.
The authority said testing would be available to everyone over the age of two and it was also launching community drop-off points for people to pick up and drop off tests.
Dr Agboola said: "Our additional measures are not intended to create undue anxiety but we do need to take this action in and around the Abbey and Wembrook wards to protect the community and do all we can to eliminate transmissions as we move along the roadmap out of lockdown."