Sir Michael Wilshaw, the chief inspector of schools in England, has given his "full support" to schools and colleges which "decide to take a stand against the inappropriate wearing of the veil", the Press Association reported.
Education Secretary Nicky Morgan has previously backed schools that want to ban Muslim girls from wearing face veils and suggested teachers should also be barred from wearing the garments.
Sir Michael said Ms Morgan was right to support 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.
"I have also made clear to my inspectors that 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, they should give consideration to judging the school as inadequate.
Sir Michael said he was determined to ensure "discrimination, including on the grounds of gender, has no place in our classrooms".
He added: "We want our schools, whether faith schools or non-faith schools, to prepare their pupils equally for life in 21st century Britain. We need to be confident our children's education and future prospects are not being harmed in any way."
His comments come after Ms Morgan said uniform policy is "very much up to schools" and head teachers have the right to decide if they want to ban the veil.
David Cameron has also said he would back institutions that have "sensible rules" over Muslims wearing full-face veils.
But the Prime Minister ruled out of imposing a French-style ban on full-face veils in public as part of a drive to build community integration and counter extremism.
Sir Michael told BBC2's Newsnight last week that he would back banning veils and said school inspectors had found the covers were causing communication problems in the classroom on occasions.
He said: "The Prime Minister's view that we have got to make sure that our liberal values, our liberal West values, are protected, people need to listen to that.
"The Muslim community needs to listen to it as well. We have come a long way in our society to ensure that we have equality for women and that they are treated fairly. We mustn't go backwards."