Schools in England must set online filters and monitor pupils' internet use under plans to protect them from radicalisation, education secretary Nicky Morgan said.
Ministers are concerned young people could be targeted by extremists, possibly via school computers.
Mrs Morgan said some pupils had been able to access information about so-called Islamic State at school.
Teaching unions said schools would welcome greater clarity on the plans.
The reforms, which have been published for consultation, follow several cases where school children either travelled, or attempted to travel, to Syria.
In February, Bethnal Green Academy schoolgirls Shamima Begum and Amira Abase, both 15 at the time, and Kadiza Sultana, then 16, flew from London to Istanbul en route to Syria.
Their head teacher has said there is no evidence they were radicalised at school as pupils cannot access social media on the academy's computers.
The three girls passing through airport securityImage copyrightMetropolitan Police
Image caption
Shamima Begum, Amira Abase and Kadiza Sultana travelled to Syria in February
Mrs Morgan said: "As a parent, I've seen just what an important role the internet can play in children's education. But it can also bring risks, which is why we must do everything we can to help children stay safe online - at school and at home."
The proposed measures include showing young people how to use the internet responsibly and making sure parents and teachers are able to keep youngsters safe from exploitation and radicalisation, she added.
The reforms will also address other issues such as cyberbullying and pornography, the Department for Education (DfE) said.
Many schools already have systems in place to filter and monitor pupils' online activity, but the new guidelines are designed to strengthen requirements to keep children safe and spot concerns quickly.
'Greater clarity'
The National Association of Head Teachers (NAHT) said schools are "doing many of these things anyway", but they would welcome "greater clarity" on how to deploy appropriate filters and monitoring systems.
"We hope school leaders will be supported in delivering [the plans]: making PSHE [personal, social, health and economic education] compulsory could free up the appropriate time within the school day to address this important issue," said Sally Bates, a head teacher and the NAHT's chair of policy.
She told the BBC schools may have to "rethink" the way they deal with technology, such as restricting pupils' use of mobile devices in secondary schools, but she added that the government should also be adopting a wider approach to regulating the internet to safeguard children outside of school.
Malcolm Trobe, deputy general secretary of the Association of School and College Leaders, said it was essential for schools and colleges to review security systems regularly, keeping with rapidly changing methods of getting through firewalls that are meant to block access to certain online content.
The latest move comes just a week after ministers announced a crackdown on unregistered schools.
Ofsted was told earlier this month to prepare cases for prosecution against 18 unregistered schools, and all future cases, in a push to stop pupils being exposed to extremist ideology.
The results of the consultation and the DfE's response will be published in the spring.