The program is an Obama-era policy that defers deportation for some undocumented youth who had been brought to the United States as children.
The Supreme Court's order is a setback for challengers, including California and the regents of the University of California, who contend that the Trump administration violated federal law when it abruptly decided to rescind the program. The challengers had sought the documents to bolster their case, pending in California.
Justice Stephen Breyer, joined by the three other liberal justices, dissented from the court's order. Stressing that the lower court has still not heard the merits of the case, Breyer criticized the majority for intervening "in this kind of discovery-related dispute."
He said the matter should be left with the lower courts, which are in a better position "to understand whether a particular discovery order is over-burdensome. "
"This court," Beyer wrote, is "poorly positioned to second-guess district courts' determinations in this area."
The high court's action is a win for government lawyers, who argued in court papers that the "district court's orders mandating discovery and expansion of the administrative record were in excess of the district court's authority."
In a statement, a Justice Department spokesman praised the Supreme Court's order.
"The Department of Homeland Security acted within its lawful authority in deciding to wind down DACA in an orderly manner, and the Justice Department believes the courts will ultimately agree," said spokesman Devin O'Malley.
California Attorney General Xavier Becerra responded: "What is the Trump administration trying so hard to hide?
"The administration owes the American people a real explanation for its decision to upend the lives of 800,000 Dreamers, stripping them of their ability to work and study, stirring fear, and threatening our economy," Becerra said. "We'll keep fighting in court for Dreamers, particularly the 1-in-4 DACA grantees who call California home."
The district judge had filed a statement with the justices arguing that the government's petition "leaves the incorrect impression that the district court endorsed unfettered discovery," he said.
Judge William Alsup of the US District Court for the Northern District of California argued that his request was "limited, narrowly directed, and reasonable."
The challengers have until Wednesday to respond to the ruling. The district court is set to hear arguments December 20 on whether the case should be dismissed altogether.