A cluster of families in Telford have tested positive for a mutation of the UK Covid-19 variant, a council said.
The cases were identified in schools, but Telford and Wrekin Borough Council reassured residents schools in the area were safe.
The local authority urged families with school-age children in the Hadley and Leegomery areas to get tested.
Public health officials are tracing contacts of the positive cases, who are said to be self-isolating.
"When cases are identified in schools this often indicates what is happening in the wider community," Liz Noakes, the area's director for public health, said.
"For this reason everyone in the local community needs to be alert."
The cases are believed to be linked, Musarrat Afza, from Public Health England (PHE), said.
"PHE is monitoring the situation closely and all necessary public health interventions are being undertaken."
A testing centre will be opened at the Telford Cultural and Leisure Centre in Hadley from Saturday.
"Overall coronavirus cases in Telford and Wrekin remain low, but we do need to closely monitor this mutation locally," Ms Noakes said.
PHE said there was no evidence that the mutation causes more serious illness.