WASHINGTON—The Supreme Court granted President Trump’s emergency request to suspend enforcement of a congressional subpoena seeking his financial records from his accounting firm, a move that could keep the documents from House Democrats for months—if they see them at all.

But in tandem with blocking the subpoena for now, the court signaled Mr. Trump would have to move quickly with his appeal, ensuring the president can’t delay proceedings through the 2020 election.

The high court’s action also makes it likely that the justices will agree to a full review of the president’s appeal after he files a formal petition with the court next month. Given the magnitude of the constitutional questions involved, the court’s decision to give Mr. Trump time to mount the appeal doesn’t come as a surprise.

The justices, in a brief written order on Monday, stayed an October appeals court ruling that upheld a subpoena by the House Oversight Committee to Mazars USA LLP. The committee is seeking eight years of financial records about Mr. Trump and his affiliated businesses as part of its probe into White House ethics issues, including whether the president is improperly profiting from his office.

Mr. Trump has said the Democratic-controlled House is using the subpoena as a political weapon that isn’t tied to any legitimate legislative purpose. The House panel said Mr. Trump is engaged in a legal assault on the authority of a coequal branch of government to hold the White House accountable for its actions.