Just under one in six secondary schools in England have been forced to send some pupils home due to suspected Covid-19 cases.
About 16% of secondaries were affected with partial closures in the week ending 24 September - double the rate the previous week.
The statistics are based on an official Department for Education survey.
Head teachers said they were "extremely concerned" at the drop in the number of fully open schools.
Some 6% of England's 23,000 schools overall were affected this week, up from 4% the previous week.
Schools are considered fully open if they are able to provide face-to-face teaching for all pupils on roll for the whole school day and they have not asked a group of pupils to self-isolate.
Where schools are not fully open, most pupils are still attending, the DfE said.
When pupils are unable to attend school because they are complying with clinical or public health advice, schools are expected to be able to immediately offer them access to remote education.
In primary schools, the rates affected by real or suspected cases are lower.
'Schools at frontline'
Only 5% of primary schools reported sending pupils home to limit the spread of the disease.
The official guidance requires pupils with Covid-19 symptoms not to attend schools and to get a test.
Schools are also required to send home those pupils who may have had contact with classmates with symptoms. They are required to self-isolate until they can get tested, if they show symptoms.
Geoff Barton, General Secretary of the Association of School and College Leaders, said he was extremely concerned at the rise in the number of partially closed schools.
"This reflects the extremely difficult circumstances in which schools are operating amidst rising infection rates in the community.
"While there are some signs of improvement in accessing Covid tests and obtaining timely public health advice in the event of positive cases, we continue to receive reports from schools that problems persist, and this is not good enough."
7.2m pupils in school
He added: "It is increasingly clear that schools have effectively found themselves on the frontline of managing the public health emergency, as well as delivering education, and the support simply has to be there."
He also called for the government to reimburse schools for the costs involved in implementing safety measures and to clarify its plans for next summer's national exams.
But Education Secretary Gavin Williamson said: "It is encouraging to see that the vast majority of schools remain open, with more than 7.2 million pupils estimated to be attending schools last week gaining all the benefits of being in the classroom.
"Only a small minority of pupils are currently self-isolating and there is remote education provision in place for the short time they are unable to attend school.
"I'm hugely reassured schools have the right protective measures in place to reduce the spread of the virus, and are only asking close contacts of confirmed cases to self-isolate.
"I want to thank teachers and leaders for all they are doing to make sure pupils can access the education they deserve."