The safeguards could stop children like Shamima Begum, Kadiza Sultana and Amira Abase becoming radicalised.
By Jon Craig, Chief Political Correspondent
All schools are to be ordered to protect children from harm online - including cyberbullying, pornography and the risk of radicalisation - under new Government plans.
The Education Secretary, Nicky Morgan, says recent events have shown that the risks to young people being targeted by radical groups have risen and should not be underestimated.
She claims some school children who travelled or attempted to travel to Syria - such as three teenage girls from Bethnal Green, East London - were able to access material about Daesh and foreign fighters via school computers.
Shamima Begum, Kadiza Sultana and Amira Abase were all pupils at Bethnal Green Academy.
They travelled to Syria and at least two of them have become so-called "jihadi brides" with Islamic State militants.
So, under proposals for consultation, all schools will:
:: Need to have appropriate filters and monitoring systems, so that no child can access harmful content via the school’s IT systems and concerns can be spotted quickly.
:: Be required to ensure that they teach their pupils about safeguarding, including online.
"As a parent I've seen just what an important role the internet can play in children’s education," says Ms Morgan.
"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.
"This includes ensuring young people know how to use the internet responsibly and that parents and teachers have the right measures in place to keep children safe from exploitation or radicalisation.
"These measures are delivering on the Government’s commitment to keep children safe from harm, as well as providing helpful support and information for professionals and parents so we are all equipped to help protect children in this digital age."
The Government is also announcing a further package of measures to help keep children safe online, including:
:: Two guides on social media - one for social media companies on good practice, and one to help parents keep their children safe.
:: New online training will be launched in the new year for professionals, including nurses, doctors and teachers who work with children and young people.
Welcoming the Government’s proposals, David Wright, Director of the UK Safer Internet Centre, said: "It’s great that online safety is being incorporated into this document.
"The UK Safer Internet Centre is ready to work with the Department for Education to explore how best to support schools in meeting this new requirement."