Hawaii District Judge Derrick Watson ruled there was a strong likelihood that "irreparable injury is likely if the requested relief is not issued".
He also pointed to "questionable evidence supporting the government's national security motivation".
His ruling prevents the President's executive order restricting travel to the US from Muslim-majority countries from going into effect today.
Mr Trump immediately hit out against the decision, claiming it was "flawed" and an example of "unprecedented judicial overreach".
He said the court's decision "makes us look weak" and said he was prepared to fight it all the way to the Supreme Court if necessary.
More than half a dozen states have been trying to stop the ban, and federal courts in Maryland, Washington state and Hawaii heard arguments on Wednesday about whether it should come into force.
Hawaii argued that the ban discriminates on the basis of nationality and would prevent Hawaii residents from receiving visits from relatives in the six countries covered by the ban.
The state also said the ban would harm its tourism industry and the ability to recruit foreign students and workers.
The judge was nominated to the federal bench by Barack Obama in 2012 and is currently the only Native Hawaiian judge serving at that level.
Donald Trump has said the restrictions on all refugees and people from Iran, Libya, Somalia, Sudan, Syria and Yemen are needed to prevent extremists from entering the US.
He was boosted by a ruling from a federal appeals court judge, who said the President does have the authority to block foreign travellers and that courts should defer to his authority in decisions about who enters the country.
But at another hearing in Maryland, lawyers said the revised measure still discriminates unfairly against Muslims.
Government lawyers argued that the ban was changed to address legal concerns, including the removal of an exemption for religious minorities from the affected countries.
"It doesn't say anything about religion. It doesn't draw any religious distinctions," said Jeffrey Wall, who argued for the Justice Department.
Lawyers for the American Civil Liberties Union (ACLU) and other groups said that Mr Trump's statements on the campaign trail and statements from his advisers since he took office make clear that the intent of the ban is to ban Muslims.
Trump policy adviser Stephen Miller has said the revised order was designed to have "the same basic policy outcome" as the first.
The new version of the ban details more of a national security rationale. It is narrower and eases some concerns about violating the due-process rights of travellers.
It applies only to new visas from Somalia, Iran, Syria, Sudan, Libya and Yemen and temporarily shuts down the US refugee programme. It does not apply to travellers who already have visas.