Children and staff in three class bubbles at Sundorne Infant School in Shrewsbury have been told to stay at home after the positive tests.
The Haughmond Federation, the trust which the school is part of, has sent letters to inform parents and carers.
The school remains open for other pupils and, unless they are unwell with symptoms or have been identified as a close contact, parents are advised that their children should continue to attend.
Steph Peters, executive headteacher for the Haughmond Federation said: “Following advice from Public Health England and Shropshire Council, we have asked people who have been in close contact with the individuals who have tested positive to self-isolate.
"Strong measures to limit the outbreak were put in place within hours of this case being confirmed. We will continue to closely monitor the situation and communicate clearly with parents and students.”
Rachel Robinson, Shropshire’s director of public health, said: “We want to reassure students and parents/carers that the risk of infection is very low. The Haughmond Federation has taken all the necessary precautions to limit the spread of the virus.
“Anyone who is symptomatic will be offered immediate testing. Contact tracing is underway and if anyone is identified as a contact of a confirmed case of Covid-19, a contact advisor from Test, Trace will be in touch with appropriate advice.
“We will continue to work in partnership with Public Health England and Haughmond Federation as we continue to manage this evolving situation.
“Protecting the health of our population remains a priority, and at this time we would also like to remind everyone to follow social distancing advice to reduce their social interaction with other people.
“Good hand hygiene remains the best protection against the virus, including washing your hands more regularly with soap and water for at least 20 seconds and covering your mouth and nose with a tissue when you cough or sneeze.
“If you are showing coronavirus symptoms, or if you or any of your household are self-isolating, for example if you have been contacted as part of the test and trace programme, you should stay at home – this is critical to staying safe and saving lives.”
If you have any queries or concerns, call Shropshire Council’s Education Line on 0345 678 9008
The support line is open from 9am to 5pm, Monday to Friday. Press 5 for back to school enquiries.