Shulem Stern from Stamford Hill Shomrim said: "There is a sense of anxiety and fear amongst local parents.
“The playground is next to a Jewish Care home where many elderly Jewish residents live, some of them Holocaust survivors.
“It's a mindless act, I hope the ones responsible are caught and brought to justice."
Shomrim has urged witnesses to call the police with information.
Board of Deputies vice president, Marie van der Zyl said: “The daubing of Nazi symbols in a place where Jewish children study and play is an act of racism intended to spread fear and alarm.
“In a week when the Board of Deputies has given evidence at the Home Affairs Select Committee’s inquiry into the rise of antisemitism, this is an example of one of the many threats the Jewish community faces. We hope the perpetrators will be apprehended and made to feel the full force of the law.”
Stamford Hill, in north-east London, is home to Europe’s largest strictly Orthodox community.