The Netflix South Korean thriller series tells the story of debt-ridden people competing for a huge cash prize in a deadly series of children's games.
Its popularity prompted Central Bedfordshire Council to email parents about "aggressive" primary pupils.
They were advised to "be vigilant", as first reported by The Guardian.
The email said: "There have been some concerning reports recently about children and young people 'playing' Squid Game whilst at school.
"Squid Game is also being viewed via other platforms such as YouTube and TikTok, and given the popularity of the games in the show, developers have made various mini-games based on Squid Game on Roblox and other gaming platforms."
The Netflix series is rated 15.
The council email continued: "We strongly advise that children should not watch Squid Game. The show is quite graphic with a lot of violent content."
The council told the BBC: "Last week our education safeguarding team were made aware that some primary-aged children in one of our schools were behaving aggressively on the playground while replicating games from the Squid Game programme.
"It was felt that these young children had seen clips of the programme, which has a rating of 15 due to its graphic nature, on social media.
"Following the concerns raised, the team shared information about parental settings, and resources to support parents to keep their children safe online."