Pupils and teachers in all of England's secondary schools and colleges will be required to wear face masks in communal areas and corridors from Thursday.
New government guidance also says that "clinically extremely vulnerable" staff members should not come in to school.
Head teachers said schools would need help to pay for supply teachers.
They also expressed anger that the guidance had "landed on school leaders' desks less than 24 hours before the start of the national lockdown".
The new guidance, issued by the Department for Education on Wednesday afternoon, says "face coverings should be worn by adults and children aged 11 and above when moving around the premises, outside of classrooms or activity rooms, such as in corridors and communal areas where social distancing cannot easily be maintained", and the same applies to further education colleges.
Schools should work to implement the guidance as soon as possible, the department said, but can have until Monday 9 November if they require additional time.
Until now, this requirement was only for schools and colleges where the local Covid-19 alert level was "high" or "very high".
The DfE also says teachers with serious underlying health issues should keep away from the premises.
"Those individuals who are clinically extremely vulnerable are advised to work from home and not to go into work," the guidance says.
"Staff should talk to their employers about how they will be supported, including to work from home where possible, during the period of national restrictions.
"All other staff should continue to attend work, including those living in a household with someone who is clinically extremely vulnerable."
Paul Whiteman, general secretary of the NAHT school leaders' union, said the lockdown was announced four days ago and that it "beggars belief that schools have had to wait until now to find out how it affects them".
"Frankly, it is ridiculous that this new guidance has landed on school leaders' desks less than 24 hours before the start of the national lockdown.
"There is very little in the guidance that could not have been communicated with schools 72 hours ago."
Mr Whiteman also expressed concern about the impact vulnerable teachers staying at home would have an schools' ability to operate.
"Given the restrictions around clinically extremely vulnerable staff, the reality is that some schools may now find it increasingly difficult to remain open to all pupils."
Geoff Barton, general secretary of the Association of School and College Leaders, welcomed the move, but said: "It will mean that there are more staff missing from the workplace, on top of those who are self-isolating.
"It is imperative that the government reimburses schools and colleges with the cost of hiring supply cover for staff absence.
"We have received reports of schools having to spend £6,000 per week on supply cover, and this situation is going to become worse - schools and colleges cannot sustain these costs."
Mr Barton said the extension to the rule on face coverings was a "sensible response to rising Covid levels, and will act as an extra level of protection on top of the other safety measures in schools".
He added: "The government's education recovery planning does need to take into account the impact of these restrictions on health and wellbeing."