The cases were confirmed at Market Drayton Infant and Nursery School this week.
The school has told all possible ‘bubble’ contacts to self-isolate and the risk of infection remains low, according to Shropshire Council.
The school has informed parents/guardians/carers and staff of the situation will remain open for all other pupils.
Samantha Scott, executive headteacher at Market Drayton Infant and Nursery School said: “We have received confirmation that we have two positive cases of coronavirus within the school. In line with public health guidance, those affected have now entered self-isolation.
“We have advised anyone who came into close contact with the individuals affected to enter self-isolation for 14 days from the date of their last contact, in line with government guidance.
“As a school, we have strong Covid-19 secure measures in place, and we have taken all appropriate actions to help stop the spread of the virus.
“Parents and staff have been informed and we will continue to keep them up to date with any further actions.
“We are sorry for the disruption this will cause, and we will continue to support all pupils and staff during this time.”
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Rachel Robinson, Shropshire Council’s director of public health said: “We want to reassure students and parents/carers that the risk of infection remains low.
"The school has acted responsibly and taken all the necessary precautions to limit the spread of the virus, which in this case requires a class bubbles and members of staff to self-isolate
“Anyone from the school community and their families 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 and Trace will be in touch with appropriate advice.
“We will continue to work in partnership with Public Health England and the school as we continue to manage this particular outbreak.
“Protecting the health of our population remains a priority, and at this time we would also like to remind everyone to stay at home as much as possible, and limit your contact with people outside your household and support bubbles.
“Over the past three weeks we have not only seen a continued rise in cases across Shropshire but increasing evidence of the spread of the virus beyond people in their 20s to older and potentially more vulnerable age groups."