Acorn Nursery, which operates in the Westcroft Centre, in Milton Keynes, said that those who tested positive for coronavirus come from individual “bubbles” within the building and had been isolated.
In a statement given to the BBC, a spokesperson said: “The bubbles exposed to the confirmed cases are self-isolating and PHE have confirmed that there are no public health concerns in relation to the controls in place at the nursery as they are adhering to government guidelines.
"The nursery remains open to bubbles not exposed to confirmed cases."
The nursery is working with Milton Keynes Council and Public Health England (PHE) and said testing would be offered to all staff, pupils and parents as a precaution.
A spokesperson for PHE said there were no health concerns around the nursery remaining open.
They added: “Following government guidance, the bubbles of children and staff that may have had exposure to a confirmed case have been closed but a full closure of the nursery is not required.
"There are no public health concerns in relation to the Covid control measures in place at the nursery."