Prime Minister Kyriakos Mitsotakis said the move was aimed at tackling rising anxiety and sleep problems among young people, as well as what he described as the "addictive design" of social media.
The restriction will come into force from January of next year.
In December Australia became the first country in the world to require TikTok, YouTube, Snapchat and other top sites to remove accounts held by under-16s, or face heavy fines. France, Austria and Spain are among a growing number of nations pursuing similar curbs.
The UK government has launched a consultation on whether to implement a ban for under-16s, while Ireland and Denmark are considering similar measures.
Social media companies argue that blanket bans will be ineffective, difficult to enforce and could isolate vulnerable teenagers. Reddit is challenging Australia's law in court.
In a video message posted on TikTok on Wednesday, Mitsotakis said: "Many young people tell me they feel exhausted from comparisons, from comments, from the pressure to always be online."
He said he had spoken with parents who said their children do not sleep well, are anxious and are always on their phones.
Calling the planned restriction "difficult but necessary", he said the government's goal was not to distance young people from technology which "can be a source of inspiration, knowledge and creativity".
"But the addictive design of certain applications, and a business model based on capturing your attention - on how long you stay in front of a screen - takes away your innocence and your freedom. That has to stop somewhere."
