"Since children play these games with headphones, there is always the possibility that they are connected to people – adults play this game too – and the language they use when they are killed can be quite colorful".
Fortnite is a style game "battle royale" where up to 100 people compete at one time in online games until death.
Since its release last year the popularity of the game has exploded and announced this month that now has 200 million players.
The game can be downloaded for free, but players can spend money on cosmetic items for their online characters such as weapons and costumes, called "skins".
Hannah Beale, a four-year-old teacher at Foxmoor Primary, Stroud, who also sent letters to her parents, said the children were bullied for their Fortnite characters.
He said: "It is getting to the point where children can buy costumes for their characters and this leads to cyberbullying.
"Players are looking for characters that wear certain things – it's pretty scary where these things are going."