Judge Derrick Watson ordered that the law could not be enforced, hours before it was due to come into effect at one minute past midnight on Thursday.
His ruling applies nationwide.
Two other judges considering appeals against the ban - Judge Theodore Chuang, in Maryland, and Judge James Robart in Washington state - are yet to issue their verdicts.
But Judge Watson's ruling means that Mr Trump's travel ban is once again thrown into chaos - a decision guaranteed to infuriate the president.
At 12:01 am on Thursday, the president’s new executive order was due to suspend the US refugee programme for 120 days, halt for 90 days the issuance of new visas to people from six Muslim-majority countries and reduce the number of refugees allowed to enter the United States this year from 110,000 to 50,000.
Hawaii was the first state to announce that it would consider an appeal against the second ban, with attorneys for the state filing a new 40-page request the day after the second ban was unveiled, on March 6.
Mr Trump's first travel ban, issued on January 27 with immediate effect, unleashed chaos and was eventually blocked a week later.
In his appeal against the second travel ban, Douglas Chin, Hawaii's attorney general, said the filings asked the court to declare sections 2 and 6 of Mr Trump's executive order contrary to the constitution and federal law.
"Sections 2 and 6 of the March 6, 2017 Executive Order violate the Immigration and Nationality Act by discriminating on the basis of nationality, ignoring and modifying the statutory criteria for determining terrorism-related inadmissibility, and exceeding the President's authority under the Immigration and Nationality Act," he said.
"The new executive order is resulting in the establishment of religion in the state of Hawaii contrary to its state constitution; it is inflicting immediate damage to Hawaii's economy, educational institutions, and tourism industry; and it is subjecting a portion of the state's citizens to second-class treatment and discrimination, while denying all Hawaii residents the benefits of an inclusive and pluralistic society," they argued in court filings.
"The executive order means that thousands of individuals across the United States and in Hawaii who have immediate family members living in the affected countries will now be unable to receive visits from those persons or to be reunited with them in the United States."
Mr Chin told CNN that he had filed the report because the executive order ran contrary to Hawaii's laws and traditions.
"The entire history and culture of Hawaii is based upon nondiscrimination either in its constitution as well as its laws," he said.
"Hawaii has 20 per cent foreign-born residents and 100,000 people who are not citizens as well as 20 per cent of our workforce that are not foreign born."
Neal Katyal, one of the lead attorneys for Hawaii and former acting US solicitor general, said that the second travel ban was more legally sound than the first one. But, in his view, the new travel ban still "suffers from the same constitutional and statutory defects."