In a video message addressed to young people, Mitsotakis said children spending long hours in front of screens did not allow their minds to rest and faced growing pressure from constant comparison and online comments.
The Greek prime minister said he had spoken with many parents who reported that their children did not sleep well, become anxious easily and spent long hours on their phones.
An opinion poll by ALCO published in February showed about 80% of those surveyed approved of a ban.
The Greek government has already outlawed mobile phones in schools and set up parental control platforms to limit teenagers' screen time.
"Greece will be among the first countries to take such an initiative," Mitsotakis said on Wednesday.
"I am certain, however, that it will not be the last. Our goal is to push the European Union in this direction as well."
Australia became the world's first country to ban social media for children under 16 in December, blocking access to platforms including TikTok, Alphabet's YouTube and Meta's Instagram and Facebook.
Meta, Snapchat and TikTok have said they continued to believe Australia's ban would not protect young people but committed to complying with it.
Other countries are also tightening rules on social media with the United Kingdom, Malaysia, France, Denmark and Poland either considering a ban or in the process of legislating one.
Writing separately to European Commission President Ursula von der Leyen, Mitsotakis called for co-ordinated European Union action, arguing that national measures alone would not be sufficient to protect minors from internet addiction.
In the letter, he proposed establishing an EU-wide "digital age of majority" at 15, mandating age verification and regular re-verification for all platforms, and setting up a harmonised enforcement and penalty framework, urging the bloc to put a unified system in place by the end of 2026.
