Gillian Duckworth, director of legal and governance at the council, said: “All complaints received are taken seriously.
“We are unable to confirm details of any complaint or individuals identified in order to protect all affected parties.”
It is understood that the Labour Party is investigating but its disciplinary procedures are confidential.
A spokesman said: “The Labour Party takes all complaints of antisemitism extremely seriously and they are fully investigated in line with our rules and procedures, and any appropriate disciplinary action is taken.”
Town Hall bosses have previously said it can be difficult to reprimand councillors for unacceptable behaviour on social media despite complaints.
Councillors have to abide by a code of conduct but currently the rules say they can only be disciplined if they step out of line in their role as a councillor.
There’s a grey area with social media as to whether they are speaking as a councillor or as an individual member of the public.
Sheffield Council releases an annual list of complaints to the standards board but does not name individuals.
Any breach of the code of conduct could result in the councillor having to make a formal apology through to being barred from attending committees for up to two months. Individual political parties can also take action.