NSPCC Scotland wants pupils from early in their primary career to be taught about the dangers of online abuse and ways to avoid it.
It also wants teachers to be trained in spotting signs of cyberbullying and for special support to be given to pupils who have been victims - even when the bullying takes place outside school.
The charity made the call in a submission to the Scottish Parliament's education committee, which is holding an evidence session on cyberbullying tomorrow.
NSPCC Scotland's submission said: "Cyberbullying should be a core component of the school curriculum with a focus on the possible consequences of young people's actions online, the impact of cyberbullying and the importance of forming healthy and respectful relationships online.
"A 'whole school' approach to anti-bullying should be taken with support given to young people experiencing cyberbullying even when incidents occur outside the school gate. Teachers should also be trained in how to recognise and handle cases of cyberbullying."
ChildLine has reported an 87% increase in counselling sessions with young people on the issue of cyberbullying during 2012/13.
Last year, it emerged that hundreds of cases of cyberbullying were being reported in Scottish schools, with pupils as young as eight verbally abusing each other on social networking sites.
Figures obtained by the Scottish Conservatives showed schools recorded more than 500 incidents over the previous three years, though the real figure is likely to be higher.
The number included incidents where children filmed bullying and then threatened to put the footage online.
The figures and nature of incidents were revealed following a Freedom of Information request by the Tories to all Scottish local authorities.
Teaching unions have also called for a national campaign to promote zero tolerance of cyberbullying amid complaints that teachers themselves are being subjected to "distress and trauma" by pupils on social networking sites.
A number of high-profile cases of online abuse have previously led to calls for more action to be taken to combat the problem.
Last year, Scottish teenager Daniel Perry, from Dunfermline, jumped to his death from the Forth Road Bridge after being blackmailed online.
The 17-year-old was tricked into taking part in Skype chat with someone he believed was a girl of his own age.
In another case last year, the father of 14-year-old Hannah Smith from Leicestershire blamed online bullying after the teenager took her own life.
A Scottish Government spokeswoman said ministers believed all forms of bullying were totally unacceptable and that pupils were learning about online safety and responsible use of communication technologies under the Curriculum for Excellence.
She added: "Schools have been provided with guidance to help them develop and update policies to promote the safe and responsible use of mobile technology in schools along with an e-safety review tool to develop an action plan for improvements.
"Last week we announced new research that will investigate how online abuse and in-person bullying cross over, and the best ways to tackle it quickly and efficiently, and this will be fed in to our guidance to partners, schools and teachers."
NSPCC Scotland said: "As the technological landscape changes we must respond accordingly. Incorporating cyber-safety into the school curriculum would help to instil safe online behaviour from an early age."