White Australia, which has been seeking to register as a political party, had asked the High Court to temporarily block its designation as a prohibited hate group until a later hearing challenging the validity of the laws.
But on Thursday, the court's Chief Justice Stephen Gageler dismissed White Australia's bid for an injunction.
"This is not a case in which compelling grounds have been shown," he said in his written reasons.
While White Australia argued it would suffer "irrevocable and irreparable" harm if the laws were allowed to stand unchallenged, Justice Gageler said an injunction would do little to help.
"The difficulty for (White Australia) is that the ... relief they seek against the defendants would not remove or ameliorate that prejudice," he found.
There was a "real and substantial" risk the White Australia Party's incorporation in Victoria could be cancelled after the state's registrar of corporations issued a "show cause" notice, Justice Gageler said.
But he said the injunction sought would not address that, and party members should take separate proceedings against the state's registrar of corporations.
White Australia is also challenging the broader constitutionality of anti-hate-speech laws passed after the Bondi Beach mass shooting, with a two-day hearing scheduled for September.
Arguing for the injunction on Wednesday, White Australia's lawyer Peter King said the organisation's listing as a prohibited hate group would permanently shut it down.
"Unless restrained, there will be an extinction of the organisation," he told the High Court.
The ruling prompted a swift reaction on encrypted social media platforms among accounts sympathetic to White Australia.
In a lengthy statement on Telegram, White Australia's president Thomas Sewell said he would seek advice on whether the ruling allowed him to continue fundraising to pay for his legal representation.
An account in the name of Jack Eltis, another top neo-Nazi, said the injunction was only a procedural matter.
One Telegram account which has previously shared content from senior neo-Nazis described the ruling as "woke nonsense!"
"The wokes have gone too far," another posted.
Home Affairs Minister Tony Burke declared the neo-Nazi organisation a prohibited hate group in May after receiving advice from spy agency ASIO.
White Australia's predecessor, the National Socialist Network, announced it was disbanding when the hate laws were introduced.
In reality, Mr Burke said, the group had "phoenixed" - changing its name to White Australia and continuing operations with largely the same members.
Under the government's declaration, it is a crime to support, fund or join the group.
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