In a two-sentence order, the high court affirmed a decision by the District of Columbia U.S. Circuit Court of Appeals that the firm must pay $50,000 a day until it turns over information to the grand jury or otherwise cooperate with Mueller.
On Dec. 24, Chief Justice John Roberts put the lower court's contempt decision on hold while the full court considered the matter.
"The application for stay, presented to the chief justice and by him referred to the court, is denied," the court ruled. "The administrative stay previously entered by the chief justice is vacated."
No one dissented in the order.
"The fact that no justice publicly noted a dissent from today's order suggests that the court is inclined to stay out of this dispute altogether," University of Texas law professor Stephen Vladeck told CNN.
The high court still has to rule on a motion by the company to review its case on the merits.
In August, the company sought to quash the subpoena but Judge Beryl Howell rejected the request and imposed fines.
On Dec. 18, three members of the appeals court ordered the company to comply with the order. Four days later, the company asked the Supreme Court to stay the contempt fines.
The appeals court determined that the request was an exception to the Foreign Sovereign Immunities Act established in 1977 limiting foreign governments from being sued in U.S. courts.
The court closed a floor of the courthouse during appellate arguments so the identities of the arguing attorneys were unknown.
The appellate judges didn't mention the link between the "Corporation" and "Country A," but Politico reported in October the case involved Mueller's Russia investigation.
About 10 minutes after the court activity, CNN reported, a Justice Department car pulled into the special counsel's office building with two top Mueller attorneys.
Mueller is investigating Russian interference in the 2016 presidential election as well as possible collusion by members of the Trump campaign and possible obstruction of justice by President Donald Trump.