The children, who are from the same family, are one year apart and study at Dawley Church of England Primary School.
A letter home from principal Nick Andrews said that the advice they had been given meant that entire learning 'bubbles' did not have to isolate.
It said: "The two cases are with children in Year 2 and Year 3, who are from the same family. We received notification of the results late on Tuesday evening
"There is a clear process and protocol we must follow as a school, which involves us contacting Telford and Wrekin Health Protection Hub for advice. This does mean there can be a delay in gaining information.
"The advice given to us is that, as the children were asymptomatic (showing no Covid symptoms) there is a 48-hour period prior to them having the test, where if they have contact with others, those people may become infected.
"The tests were taken on the Monday, meaning the Saturday and Sunday were the 48 hours before. Prior to this time, the children showed no symptoms when in school.
"The advice to us was very clear that we could remain open and there was no need for any partial closure i.e. close the Year 2 and 3 bubbles.
"We understand that this advice may seem contradictory to previous advice but we advise that, as you know, this is an ever-changing virus and along with which the advice changes regularly and rapidly.
"We are very fortunate to have extremely dedicated staff, children who are following hygiene measures really well and robust Covid measures in place, which has meant we are able to stay open at present."