Four pupils at Prince George and Princess Charlotte's primary school were reportedly sent home over coronavirus fears.
The children at Thomas's Battersea , were understood to be in self-isolation as a precautionary measure following a trip to northern Italy.
However, none of the children have a confirmed case of the illness.
This comes as schools across the UK have closed to protect against coronavirus, despite health officials recommending that they should stay open.
At least eight have closed, while others have sent pupils home amid fears they may have been exposed to coronavirus during trips to northern Italy.
But Public Health England (PHE) said that its general advice is not to close schools.
The Mirror reports that the organisation's medical director Paul Cosford told Radio 4's Today programme: "Schools have to take difficult decisions given the complexity of issues that they are facing.
"What I would say is that our general advice is not to close schools."
St Thomas's Battersea is reported to have issued a statement to Spanish news site El Confidencial in which it confirmed the measures.
They said: "Like all schools, we are taking very seriously the potential risks related to the spread of Covid-19 and to this end we are following the Government's instructions to the letter on infection prevention and case management in which it is suspected that some staff member or students exposed to the virus or showing any symptoms.
"We currently have a very small number of students who have been evaluated and these individuals currently remain in their homes waiting to receive the results of their exams.
"All parents have been informed and we have maintained regular communication with our school community to ensure that councils are shared and important information circulated.
"Of course, we will preserve the confidentiality of staff and students, and we will not comment on specific cases."
Kensington Palace have been approached by the Mirror for comment on the development.
