One account using the name “Rabbi Larry” sent tweets to Ms Wolfson comparing Jews to rats, along with images of showers and a Nazi flag with the caption “free public showers for Juden”.
The Twitter user also sent other antisemitic tropes and neo-Nazi abuse.
Labour MP Wes Streeting offered the new candidate his support on social media.
He tweeted: “So sorry to see this, Rhea. Keep strong. Will report anything I see. Take care.”
Ms Wolfson, a Scottish Labour activist, has the support of the pro-Corbyn campaign group Momentum and will represent the Centre-Left Grassroots Alliance, for the place on the party’s governing body.