The new rule has been proposed by the UK's Information Commissioner Elizabeth Denham and is part of a 16-rule code which is being reviewed in a consultation which will continue until May 31.
Denham said: "This is the connected generation. The internet and all its wonders are hardwired into their everyday lives.
"We shouldn't have to prevent our children from being able to use it, but we must demand that they are protected when they do. This code does that."
The final version is due to come into affect in 2020.
The consultation follows the UK government vowing to crack down on social media and online sites that don't tackle "online harms".
Apps could be heavily fined or blocked in the country if they do not regulate hate crimes and abuse, such as revenge pornography and terrorist content, the Culture Secretary Jeremy Wright has warned.
Speaking to 'BBC Breakfast', he said: "The era of self-regulation for online companies is over.
"Voluntary actions from industry to tackle online harms have not been applied consistently or gone far enough."
On what penalties they could face, he added: "If you look at the fines available to the Information Commissioner around the GDPR rules, that could be up to 4% of company's turnover... we think we should be looking at something comparable here."
The proposed plans call for an independent regulator to inflict the penalties on social media sites like Facebook and Twitter, as well as Snapchat and even cloud storage services.
Home Secretary Sajid Javid said such apps and services have "to protect the young people they profit from".
He continued: "Despite our repeated calls to action, harmful and illegal content - including child abuse and terrorism - is still too readily available online."