WASHINGTON—A federal appeals court found the U.S. Consumer Financial Protection Bureau is funded through an unconstitutional method, a ruling that threw out the agency’s regulation on payday lenders and struck a blow against how the agency operates.

The decision, by a three-judge panel of the Fifth U.S. Circuit Court of Appeals in New Orleans, found the CFPB’s funding structure violated the Constitution’s doctrine of separation of powers, which sets the authority of the three branches of government. Congress has the sole power of the federal purse, and the bureau’s funding structure undercuts that authority, the court said.

When Congress created the CFPB through the 2010 Dodd-Frank financial overhaul law, it exempted the agency from the annual legislative appropriations process. Rather than having Congress review and vote on its budget, the bureau gets its money through transfers from the Federal Reserve, up to a certain cap. The Fed can’t turn down requests under that cap.

“Congress’s decision to abdicate its appropriations power under the Constitution, i.e., to cede its power of the purse to the Bureau, violates the Constitution’s structural separation of powers,” Judge Cory Wilson wrote for the court. All three judges on the panel were appointed by former President Donald Trump.

While other federal regulators such as the Fed are also exempt from the annual appropriations process, the judges said the consumer bureau’s funding structure “goes a significant step further than that enjoyed by the other agencies.”

CFPB spokesman Sam Gilford disputed the reasoning behind the ruling, saying other federal financial regulators are funded outside annual spending bills, as are programs such as Medicare and Social Security. “The CFPB will continue to carry out its vital work enforcing the laws of the nation and protecting American consumers,” the spokesman said.

The bureau could ask all the active judges on the appeals court to reconsider the decision or it could seek review by the Supreme Court.

Some analysts said that the ruling may have no immediate effect on the bureau’s activities while the case moves through the courts. But the bureau could see its activities significantly clipped should it ultimately become subject to the annual appropriations process.

“The scale and scope of its work could be materially narrowed,” said Isaac Boltansky, director of policy research at financial-services firm BTIG.

The CFPB has been politically polarizing since its inception, when former President Barack Obama tapped then-Harvard law professor Elizabeth Warren to set it up to protect consumers from abusive financial-industry practices on products like mortgages, student loans and credit cards.

Democrats have wanted a muscular CFPB to take on what they saw as financial-industry excesses. Republicans and Wall Street have criticized the bureau as an instrument of runaway government regulation, with too much power over a significant slice of the economy.

Consumer advocates and some former bureau officials criticized Wednesday’s ruling, saying it would likely jeopardize other rules, guidelines and enforcement actions if it’s allowed to stand.

“If this decision is not stayed, the result will be chaotic,” said Deepak Gupta, who worked at the consumer bureau during its founding between 2011 and 2012, where he served as senior litigation counsel and senior counsel for enforcement strategy. “It’s going to invite a proliferation of legal challenges to everything the bureau has done.”

Republican lawmakers cheered the ruling. “Congress should have never given up its appropriations power when establishing the CFPB,” said Sen. Cynthia Lummis (R., Wyo.) in a statement. She added that the bureau should be funded through “the normal appropriations process, not through the Federal Reserve.”

The bureau has largely survived repeated legal challenges to its creation. While a 2020 Supreme Court ruling found that the bureau’s structure was unconstitutional because its director held too much unchecked power, the court held the solution was to allow the president to remove the director for any reason. The court rejected broader legal arguments that it should strike down the bureau altogether.

The payday rule, completed in 2017 when the bureau was still under Obama-era leadership, clamped down on providers of small, short-term consumer loans that can have interest rates as high as 400%, bringing the industry under federal oversight for the first time. The bureau later repealed a key provision of the rule in 2020 requiring lenders to verify borrowers’ incomes to ensure that they can afford to repay the loans.

As part of Wednesday’s ruling, the appellate court threw out the remaining portion of the payday restrictions. While the court said the bureau didn’t exceed its authority in writing the payday requirements, it nonetheless tossed the rule as a product of the agency’s “unconstitutional funding scheme.”

Write to Andrew Ackerman at andrew.ackerman@wsj.com