The American Civil Liberties Union (ACLU) filed a case in response to the order issued on Friday.
The ACLU estimates that between 100 and 200 people are being detained at airports or in transit.
Thousands of people have been protesting at US airports over Mr Trump's clampdown on immigration.
His executive order halted the entire US refugee programme and also instituted a 90-day travel ban for nationals from Iran, Iraq, Libya, Somalia, Sudan, Syria and Yemen.
Those who were already mid-flight were detained on arrival - even if they held valid US visas or other immigration permits.
On Saturday, Mr Trump told reporters: "It's working out very nicely. You see it at the airports, you see it all over."
Other executive orders issued by Mr Trump on Saturday were:
A ban on administration officials ever lobbying on behalf of a foreign government
An order to Defense Secretary Jim Mattis to come up with a plan within 30 days to defeat so-called Islamic State
Restructuring the National Security Council with a key role for senior strategist Steve Bannon
'Irreparable injury'
The ruling, from federal Judge Ann Donnelly, in New York, prevented the removal from the US of people with approved refugee applications, valid visas, and "other individuals... legally authorised to enter the United States".
The emergency ruling also said there was a risk of "substantial and irreparable injury" to those affected.
Her ruling is not on the constitutionality of Mr Trump's executive order. What will happen to those still held at airports remains unclear.
Dreams shattered' - those affected
The feeling of injustice is so big, and this ban is so demeaning! Shame!" - Syrian scientist working on skin cancer research and living in Germany who now finds she cannot travel to Philadelphia in February to visit colleagues.
"Dreams shattered" - cardiology fellow from Jordan whose Syrian wife's family cannot come to visit in the US.
"We may try our chances with other countries" - Iranian professional in Washington DC, whose wife is now stuck in Iran.
Early on Sunday, the Department of Homeland Security said it would comply with judicial rulings but would continue to enforce Mr Trump's order.
The case was brought early on Saturday on behalf of two Iraqi men detained at JFK Airport in New York.
One worked for the US military in Iraq. The other is married to a former US military contract employee.
Both have now been released. Another court hearing is set for February.
Lee Gelernt, deputy legal director of the Immigrants Rights Project, who argued the case in court said that some people had been threatened with being "put back on a plane" later on Saturday.
Mr Gelernt also said the judge had ordered the government to provide a list of names of those detained under the order.
Judges elsewhere in the US have also ruled on the issue:
In Boston, a judge decided two Iranian nationals, professors at the University of Massachusetts, should be released from detention at Logan International Airport
An order issued in Virginia banned, for seven days, the deportation of green card holders held at Dulles Airport and ordered the authorities to allow access to lawyers
A Seattle judge issued an emergency stay of removal from the US for two people.
Criticism of Mr Trump's decision has been growing louder outside the US.
Iran is threatening a reciprocal ban on US citizens entering the country.
Chancellor Angela Merkel of Germany issued a statement saying "even the necessary, determined fight against terrorism does not justify placing people of a certain origin or belief under general suspicion".
A spokesperson for UK PM Theresa May said she "did not agree" with the restrictions, and French independent presidential candidate Emmanuel Macron tweeted: "I stand with the people fleeing war and persecution".
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