Opposition Leader Bill Shorten confirmed Mr Kurnoth would be dropped, despite resisting pressure to disendorse him last week.
"I don't think he should be our candidate any more and I understand that it is in train for him to step down," Mr Shorten told reporters in Perth.
"I hope that (Clive) Palmer is willing to do something about the 20 candidates that he's got with constitutional eligibility clouds over their head, and I hope that (Scott) Morrison can show the same certainty of purpose that I've just displayed."
On Friday, Mr Shorten publicly slapped down his "stupid" candidate, but refused to cut him adrift.
Instead, he called on Prime Minister Scott Morrison to take action in relation to the Liberal candidate for McNamara, who was forced to apologise for posting an emoji referring to his wife Chloe Shorten as a pig.
The chair of the Anti-Defamation Commission, a civil rights group, said Labor dropping support for its candidate sent a clear message that his rhetoric does not reflect the values of the party or the nation,
"The hateful comments posted by Mr Kurnoth were deeply offensive, " Dr Dvir Abramovich said.
"Such bigoted slurs and scapegoating, that are often found lurking in the darkest corners of the internet, must be forcefully rejected and repudiated at every turn."
Despite being dumped by the party, Mr Kurnoth's name will remain second on Labor's ticket for the Territory's Senate seats because the ballot papers were printed over the weekend and cannot be changed.