Kate Ramsden, who sits on the national executive council of the Unison union, is reported to have written a blog post appearing to connect the Holocaust and the Israel-Palestine conflict.
"Like many abusers, unable to reflect on their own abuse, and ending up recreating it in the abuse of others, exerting their power in those weaker than themselves because once they were the powerless," the post says.
She is also reported to have written that antisemitism allegations were "orchestrated by the wealthy establishment who do not want a socialist Labour government." Ms Ramsden works for Aberdeenshire Council.
The posts were first reported by the Jewish Chronicle, which published a front-page editorial on Thursday calling on all UK voters not to support the Labour party in next month’s general election, to show solidarity with British Jews.
It is understood that the comments came to light following due diligence on candidates carried out by the UK Labour Party, separately to the devolved selection process in Scotland.
Ms Ramsden was asked to be re-interviewed by Scottish Labour about the posts, but decided to stand down.
Neither she nor Scottish Labour have made any official comment.