The education secretary wants “fewer selfies” and more “authenticity”.
He warned of the risk of online bullying and the pressure of “negative body images” on social media.
An international report this week showed England’s schools had the worst problem with cyber-bullying out of 48 countries.
Mr Hinds says he wants social media companies, celebrities and online influencers to “take their responsibility more seriously” in protecting young people from bullying or harmful content on the internet.
He pointed to a report from the OECD think tank on Wednesday which showed head teachers in England were more likely to face problems with online bullying than in any other developed country.
In England, 27% of school heads had to deal every week with the consequences of cyber-bullying among pupils, compared with an international average of 3%.
The OECD’s education director, Andreas Schleicher, said it was not right to expect head teachers to cope with pressures from the misuse of social media. There needed to be clearer regulations to support schools.
“I don’t think it’s something we can ignore and let individual schools sort out,” said Mr Schleicher.
Mr Hinds called for social media celebrities to think more about “what they are putting on their platform. Is it honest? Is it authentic? Is it too image focused?”
He said the round-the-clock presence of mobile phones added to the pressure and that no one was “immune from online cruelty”.
“All bullying is shameful but cyber-bullying is particularly cowardly and pernicious,” said the education secretary.
But he said lessons about relationships, which will become part of the curriculum next year, will teach young people about the “importance of safe and acceptable behaviour online”.