The decision means that travellers from the six Muslim-majority countries covered by the ban will still be able to travel to the US.
US District Judge Derrick Watson put an emergency stop to the new order in response to a lawsuit filed by the state of Hawaii, which argued the order discriminated against Muslims in violation of the constitution.
The new ban, signed by the President on March 6, had aimed to overcome legal problems with a January executive order that caused chaos at airports and sparked mass protests before a Washington judge stopped its enforcement in February.
Like the current one, the earlier ban barred citizens of Iran, Libya, Syria, Somalia, Sudan and Yemen from entering the country for 90 days, but it also included Iraq, which has since been taken off the list of banned countries.
Refugees were blocked from entering the country for 120 days in both orders, but an indefinite ban on all refugees from Syria has now been dropped.
The revised ban also allows in legal permanent residents and existing visa holders, providing a series of waivers for various categories of immigrants with ties to the United States.
Mr Trump said the policy was critical for national security and did not discriminate against any religion.
More than half a dozen states have been trying to stop the new ban, and federal courts in Maryland, Washington state and Hawaii have heard arguments about whether it should be put into practice.
Hawaii, and other opponents of the ban, have claimed the motivation behind it was Mr Trump's campaign promise of "a total and complete shutdown of Muslims entering the United States".
Mr Trump later toned down that language and said he would implement a policy of "extreme vetting" of foreigners coming to the United States.
Government cautions against looking for secret motives
Hawaii argued the ban discriminated against people based on their nationality and would prevent residents of Hawaii from receiving visits from relatives in the six countries covered by the ban.
The state also said the ban would damage its tourism industry and the ability to recruit foreign students and workers.
Judge Watson's ruling was handed down less than two hours after hearing the state's arguments.
In its court filings, the Government cautioned the court against looking for secret motives in the executive order and against performing "judicial psychoanalysis of a drafter's heart of heart".
Judge Watson said he did not need to do that, because evidence of motive could be found in the President's public statements.
He concluded that while the order did not mention Islam by name, "a reasonable, objective observer ... would conclude that the executive order was issued with a purpose to disfavour a particular religion".
The ruling also cited "questionable evidence supporting the Government's national security motivation".
Legal block 'makes us look weak': Trump
Speaking at a rally in Nashville, Tennessee, Mr Trump said the judge's legal block "makes us look weak" and represented "unprecedented judicial overreach".
He said he would take the case "as far as it needs to go", including to the Supreme Court.
Republican Speaker of the US House of Representatives Paul Ryan said the ban was needed to improve vetting of people entering the US, and that he had no doubt it would be upheld by higher courts.
The legal battle is likely to move now to the federal appeals circuit and could eventually get to the US Supreme Court.
Judge Watson's order is only temporary until the broader arguments in the case can be heard.