Short Wood Primary School contacted parents yesterday after learning of the positive tests, and the school leadership continues to work with Telford & Wrekin Council.
The council released a statement which said: "We can confirm that there have been four cases of Covid-19 involving pupils from Short Wood in Telford.
"The parents of pupils within the affected learning bubbles have been contacted and told they need to isolate.
"All parents were contacted directly yesterday to reassure them that the school has taken all necessary steps.
"The school remains open. Telford & Wrekin Council and the school are monitoring the situation."