Principal Yvonne Crilly of Woodlands Primary School in Ironbridge Road, Telford, has written to parents to urge them to make sure children are staying at home and not mixing, following reports of youngsters playing out, visiting friends' homes and going to the supermarket.
She also raised concerns about secondary school students who were trying to gain access to Woodlands, despite being told to self-isolate.
In the letter, she wrote: "As you are all aware, schools all over the borough are working extremely hard to ensure that pupils attending schools in Telford and Wrekin, continue to stay safe during this pandemic. We are doing our utmost to ensure that we can reduce the risk of transmission in and around school during this time.
"Self-isolation is about protecting others and slowing down the spread of Covid-19.
"It is very important that anyone who has the virus, or might have been exposed to it, limits the number of people they come into contact with for 14 days.
"This is the most effective way of preventing coronavirus from spreading.
"I am saddened that the staff and I feel we need to remind our community about these guidelines again, as I am fully aware that the large majority of us are following the rules and helping to prevent transmission.
"However, we have had, a number of reports of children and members of their family that should be isolating, playing out in the community with others, visiting friends’ homes and local supermarkets. We have also had secondary pupils that we know should be in isolation due to bubble closures, attempt to gain access to our school site.
"I am therefore asking you all once again, to help us to help you, by doing your best to follow the guidance and help to prevent any outbreaks."
Woodside councillor Greg Spruce added: "To read students told to isolate from secondary schools attempting to access the school site beggars belief.
"We all have a duty to protect ourselves and " look out for our own" in Woodside.
"Going out and breaching isolation is furthering the spread of the disease and putting lives at risk, directly and indirectly from Covid-19.
"You are also at risk of a £10,000 fine from the police. It also means lockdown regulations could last longer and become more severe.
"We have to pull together as a community and get through this.
"Please Woodsiders, do the right thing and beat this virus!"