Kathy Wiles, who had been selected as the party's candidate for Angus just 24 hours earlier, handed in her resignation after tweeting an image of the Hitler Youth around a Nazi flag in relation to a protest outside BBC Scotland on Sunday afternoon.
Labour said Ms Wiles had made the right decision and said it would "take robust and immediate action" against any member falling beneath its expected standards in the independence debate.
Ms Wiles had previously apologised for the tweet, which was posted during a conversation with leading Labour activists on social media, claiming she wanted to highlight the dangers of using children in political campaigns.
However, it sparked interest in the former academic's other social media postings, including comments on opposition students with overseas visas voting in the Referendum and claims SNP voters wanted to live off benefits.
In one Facebook post Ms Wiles, who runs an advocacy charity in Arbroath, states: "Under the referendum rules a tiny minority of the resident population (be they Chinese, Ukranian or Polynesian) can disenfranchise me from my nationality forever.
"My point about overseas voters is this: many of them e.g. Chinese students, would happily tick yes to independence because it is something they will never have, and they cannot hope to understand the complexities involved in breaking up a 300/200 year Union."
By mid-afternoon yesterday Ms Wiles' Facebook account had been deleted.
SNP MSP Graeme Dey described the Hitler Youth tweet as "extremely offensive and abusive" but that her decision to quit was one for her.
Mr Dey also claimed Ms Wile's attempt justify her tweet "made no sense at all" as Better Together pamphlets featured children on its front cover.
He added: "Ms Wiles also said other unacceptable things. She also raised concerns about the fact that Chinese, Ukrainian and Polynesian people fully resident in Scotland can vote in the referendum, and she implied that people who vote SNP are benefit scroungers. It just isn't on.
"Labour are very quick to point out faults on the other side, and we are absolutely clear that all online abuse is totally unacceptable. In light of this sorry episode, it is time for Johann Lamont to show that Labour agree."
Ms Wiles apologised through her Twitter page yesterday morning, stating: "My intention was to make a point about the dangers of using young children in political campaigns, not to make any inference about those in the photo."
A Scottish Labour spokesman said: "We will move swiftly to get another candidate in place."