Joel Nathan, chairman of Brady Maccabi, which is based in north London, said the incident had been reported to police and the Community Security Trust (CST).
One parent of a Brady Maccabi player, who wished to remain anonymous, said he and others were left “fuming and very upset” after reading the messages.
He said: “They were quite shocking. We’ve never had anything like this before in football. It’s very upsetting.”
Olympiacos club president, Andy Koullas said he was not aware of the incident but would investigate.
A CST spokesman said: “CST will support our partners at the police, FA and Kick It Out to look into this allegation with the seriousness it deserves.”
The London Football Association said it was investigating the matter.
