Ofsted has warned schools that they risk being judged "inadequate" by inspectors if pupils or staff are allowed to wear the veil.
Sir Michael Wilshaw, the Chief Inspector of Schools in England, said the organisation would support heads who "take a stand against the inappropriate wearing of the veil".
Britain does not have rules banning the veil or other religious dress in schools, unlike institutions in France for example.
But last week the Education Secretary, Nicky Morgan, said individuals schools should be free to introduce "sensible" rules on the issue of face coverings.
Sir Michael said he had ordered inspectors to consider judging schools inadequate "where leaders are condoning the wearing of the face veil by staff members or by pupils when this is clearly hindering communication and effective teaching".
He said that while discrimination has "no place in our classrooms", Ofsted needed to be confident "children's education and future prospects are not being harmed in any way".
"The Prime Minister and Secretary of State are right to give their backing to schools and other institutions which insist on removing face coverings when it makes sense to do so," he said.
"I am concerned that some heads and principals who are trying to restrict the wearing of the full veil in certain circumstances are coming under pressure from others to relax their policy. I want to assure these leaders that they can rely on my full backing for the stance they are taking."
