Kathy Wiles, who had been selected as the party's candidate for Angus just 24 hours before, handed in her resignation this morning 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 opposition students with overseas visas voting in the referendum, and claims SNP voters wanted to live off benefits.
In one Facebook post she 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."
In response to another Facebook post that the SNP wanted "interdependence not independence", she responded: "And most of the people voting for him just want dependence - benefits, benefits and more benefits."
SNP MSP Graeme Dey described the Hitler Youth tweet as "extremely offensive and abusive" but said that her decision to quit was one for her.
He added: "Ms Wiles also said other unacceptable things. In online postings, 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."
A Scottish Labour spokesman said: "We believe that Kathy Wiles has taken the right decision to withdraw in Angus and we will move swiftly to get another candidate in place.
"The debate about Scotland's future should be held in a respectful and positive way and we will take robust and immediate action if any of our members fall below these standards."