The court dissolved a temporary stay that had been put in place by Chief Justice John Roberts. In a short order, it did not give a reason for the decision, nor did it note any dissents.
The entity that is the subject of the cloaked legal battle - known in court papers simply as a "Corporation" from "Country A" - is a foreign financial institution that was issued a subpoena by a grand jury hearing evidence in the special counsel investigation, according to two people familiar with the case.
It is thought to be the first time that an aspect of Mueller's wide-ranging probe into Russian interference in the 2016 campaign has reached the Supreme Court.
Last year, a federal court in Washington ordered the corporation to pay a daily fine until it complied with the subpoena, according to court records. An appeals court panel upheld that decision last month, prompting the company's lawyers to appeal to the Supreme Court.
Late last month, Roberts, who receives emergency petitions from the D.C. Circuit, put the order and the fines on hold until the justices could consider the matter.
The secret nature of the case has prompted a Washington guessing-game about the information that Mueller is pursuing.
In the lower courts and at the Supreme Court, details of the legal battle to get information from the corporation have been sealed. At one point an entire floor of the U.S. Court of Appeals for the D.C. Circuit was closed to the public to protect the identity of the litigants.
On Dec. 18, a panel of the U.S. Court of Appeals for the D.C. Circuit issued a vaguely worded decision that solved at least part of the mystery.
"The grand jury seeks information from a corporation owned by Country A," the three-page opinion stated. The company had sought to quash the subpoena by arguing it is protected from such demands under the Foreign Sovereign Immunities Act and that complying with the subpoena would cause the company to violate its own domestic laws, according to the opinion.
The appeals court disagreed, saying that in this case, prosecutors have met their burden. The judges, in the unsigned opinion, said there was reason to believe the evidence prosecutors are seeking relates to an act "outside the territory of the United States" but one that also had "a direct effect in the United States."
A lower-court judge already had sided with the U.S. prosecutors and against the company, according to the ruling.
"When the corporation failed to produce the requested information, the court held the corporation in contempt, imposing a fixed monetary penalty to increase each day the corporation fails to comply," the appeals court noted.
In its ruling, the appeals court was particularly dismissive of the claims that the unidentified country's domestic laws barred compliance with the subpoena.
"The corporation has fallen well short" of meeting the legal requirement for such a claim, the court wrote. "The text of the foreign law provision the corporation relies on does not support its position," and statements from one of the country's regulators and the company's own lawyer "lack critical indicia of reliability," the ruling said.
For that reason, the appeals court concluded, "We are unconvinced that Country A's law truly prohibits the corporation from complying with the subpoena."
That suggests that whatever the company's identity, it is not one that has a significant business presence in the United States, because foreign firms operating in America typically comply with demands from U.S. authorities for evidence.
At the Supreme Court, the case is simply titled In Re Grand Jury Subpoena.