The education secretary said the measure is part of contingency plans being drawn up by his department to ensure lessons continue over the coming months.
His comments came after figures published over the weekend suggested one in 20 secondary-age children in England were infected with the virus last week.
The Covid rate, which came from Office for National Statistics data, was the highest of any age group reported since the pandemic struck in March 2020.
Children are classed as very low risk and their chances of becoming seriously ill are extremely rare.
Speaking at a Conservative Party fringe event hosted by the centre-right think tank Policy Exchange on Sunday, Mr Zahawi said his priority was to ensure children don't miss out on crucial lessons.
He said: “On face masks, you know we have contingency plans in the department.
“If we see further disruption my very strong focus has to be to protect education.”
He added: “We have got contingency plans to make sure that education remains open because, actually, what they told us is they really value being back at school with their schoolmates, in front of a teacher learning, and letting those creative juices flow.”
Face coverings and masks had been recommended in schools following the return of pupils to the classroom in March. But they were scrapped on 17 May as Covid restrictions began to ease as part of the UK's roadmap out of lockdown.
Critics of children wearing masks in schools said they disrupted learning by obstructing communication. Teachers, however, warned the decision to remove face coverings was hard to reconcile with the evidence on safety.
Masks do not offer full protection against the virus but they do help to limit its spread, multiple studies have shown.
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