Marianne Tellier, who was branch secretary of Park & Arbourthorne Ward only a matter of weeks ago, posted a tweet in reference to the Nazi Auschwitz concentration camp.
The post shows a Jobcentre sign with a phrase 'arbeit macht frei' which in German means 'work sets you free' - a slogan used by the Nazis and is sighted on the gates of the former Polish death camp.
It is thought she was referencing Government policy on getting people back into work.
The tweet has since been deleted.
One senior Sheffield Labour source denounced the post called the tweet 'dangerious' and was 'anti-Semitic in every sense'.
The Star understands the tweet was reported by a fellow Labour member from Sheffield Heeley CLP and the national party is aware of the post.
Sheffield Heeley MP Louise Haigh is said to be pressing Jeremy Corbyn's office to respond.
A senior Sheffield Labour official told The Star: "What the hell was she thinking? This isn't helpful in the current toxic climate that Labour is dealing with nationally.
"This is highly provocative, grossly offensive and dangerous - this is anti-Semitic in every sense. These comments are not welcome in the Labour party at all."
Liberal Democrat leader on Sheffield Council, Shaffaq Mohammed, called on Labour to address the issue.
He said: "
“This is absolutely appalling imagery and I expected better from the Labour Party. We look to those in power to set an example.
“Anti-Semitism cannot be tolerated and it’s clear from this Labour member’s Twitter profile that action needs to be taken now.”
Ms Tellier has been contacted for a comment.