They might also be asked to provide online lessons to pupils stranded at home or work in other schools to keep services going. But sick staff would be "positively encouraged not to come into work".
The startling realities behind a worldwide flu emergency follow the recent warning from the World Health Organisation that a pandemic, which may come in two or more waves several months apart, is both "inevitable" and "imminent".
Issuing guidance this week, the Scottish Executive has told local authorities to prepare their plans for dealing with pandemics, each of which could last two to three months across Britain. "Our first priority in a pandemic would be the welfare of children," it states.
Evidence from seasonal flu suggests children secrete larger quantities of the virus and for longer than adults, which can lead to rapid infection when in nurseries, childcare centres and schools.
Authorities are advised, however, to keep schools open for as long as possible. "Closure could either be very localised and brief - for example, a school with too few staff to operate safely - or more widespread and for a longer period if national public health advice confirms that this will reduce the spread of infection among children," they are told.
Following recent advice on dealing with E. coli outbreaks in nurseries, authorities are being asked to ensure schools are fully aware of rigorous but simple measures to control infection, including washing hands with hot water and soap.
Authorities, the executive reveals, already have powers during emergencies to provide education other than at school. In a pandemic, councils might not provide a full service but offer "a reasonable level of education for all children in their area if pupils are unable to attend schools due to school premises being closed to pupils during term time".
One option would be BBC Jam, the BBC's new broadband learning service for 5-16s, which will be available from September.
Headteachers are also invited to start preparing now for the practical details of coping with a pandemic. This would include support for staff or pupils who are bereaved. Further advice on online education and the impact on national exams is to follow.
In the independent sector, boarding schools are asked to set up small "family-type" units for pupils unable to return home.