WASHINGTON— Robinhood Markets Inc. has for years given customers a free share of stock for opening an account or referring friends. The practice could soon cost the online brokerage a lot more money.

Brokerages like Robinhood are required to deliver proxy materials to a public company’s shareholders ahead of annual meetings. They are then reimbursed by the public company for the cost of distribution.

This means that Robinhood’s stock giveaways have saddled some companies with larger bills for delivering proxy statements. Now, the practice is sparking a backlash from companies and scrutiny from market regulators.

One company pushing back is Florida-based drugmaker Catalyst Pharmaceuticals Inc., which says Robinhood’s program cost it more than $200,000 last year and could be even more expensive this year.

“Catalyst has become aware that Robinhood has been giving away shares of Catalyst’s common stock at no charge as part of its promotional program,” Catalyst Chief Executive Patrick McEnany wrote in a June comment letter to the Securities and Exchange Commission. “Catalyst believes that there are likely numerous companies facing this same issue, and that the costs of distributing materials to small stockholders under these circumstances is onerous and unreasonable.”

Following this and other letters, on Aug. 13, the SEC approved a proposed rule change from the New York Stock Exchange that prohibits brokers from seeking reimbursement from companies for delivering proxy materials to investors who received shares from their broker at no cost.

The new rule won’t immediately affect Robinhood, which isn’t a member of the NYSE.

But companies are now urging the Financial Industry Regulatory Authority, or Finra, which oversees brokers including Robinhood, to pass a similar rule change.

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“We don’t expect the reimbursement exemption to impact us significantly, even if it were to be adopted by other regulators,” a Robinhood spokesman said. “Customers love our free-stock program and we think it fits squarely into our mission to democratize finance for all.”

If Finra follows the NYSE’s lead in barring Robinhood from seeking reimbursement, it would be the latest in a string of regulatory actions targeting the fast-growing broker’s business practices.

Earlier this year, Finra fined Robinhood nearly $70 million to resolve allegations that it misled customers, approved ineligible traders for risky strategies and didn’t supervise technology that failed and locked millions out of trading. Separately, the SEC is reviewing Robinhood’s and other brokers’ practice of sending customers’ stock orders to high-speed trading firms in exchange for cash—a practice known as payment for order flow.

Last fall, Catalyst learned that the number of people who owned its stock had soared over the previous year to 280,000 from 25,000. The 74-employee company received a bill from a Robinhood service provider for $234,000 to cover the costs of sending out proxy materials to investors ahead of its 2020 shareholder meeting, up from $12,500 in 2019.

Another company, Marathon Oil Corp. , discovered that its shareholder ranks increased nearly 32-fold from 2019 to 2020 and that its proxy-distribution costs were 25 times higher.

Both companies launched investigations to determine the cause. They found that most of the new investors held tiny stakes through Robinhood.

Marathon Oil said its proxy-distribution costs were 25 times higher in 2020 than in 2019.

Photo: Jennifer hiller/Reuters

As one of its main marketing strategies, Robinhood randomly assigns a free share to users who link a bank account for the first time or refer a friend to its app. Robinhood users claimed $78.7 million in shares under the program in 2020, up from $29.4 million in 2019, as its customer base swelled during the coronavirus pandemic.

While the stocks are selected randomly from Robinhood’s inventory and might be valued as high as $225 a share, customers have a 98% chance of receiving a share priced between $2.50 and $10, the broker says.

In Marathon’s case, its shareholder ranks surged after its stock price fell to $3.12 from more than $13 between the start of 2020 and late March that year, as the pandemic battered energy companies. In other words, the company said, a falling share price ended up leading to “extraordinarily high” proxy-related costs at a time when it needed to cut expenses.

The brokerage app Robinhood has transformed retail trading. WSJ explains its rise amid a series of legal investigations and regulatory challenges as it looked forward to its IPO. Photo illustration: Jacob Reynolds/WSJ The Wall Street Journal Interactive Edition

“Not long after MRO became aware of this correlation, an MRO employee saw a Facebook advertisement offering free shares of stock upon opening a Robinhood account,” Marathon General Counsel Kim Warnica wrote in an April comment letter to the SEC, using the firm’s ticker symbol. “Additionally, the Corporate Secretary’s office was made aware of two individuals who received a free share of MRO stock as a result of the Robinhood program.”

Securities lawyers say it is common for Finra to follow the NYSE’s lead on proxy-related issues, given that the exchange hosts a large number of public companies.

A Finra spokesman said the agency is reviewing the SEC’s decision.

An SEC spokeswoman declined to comment.

—Alexander Osipovich contributed to this article.

Write to Paul Kiernan at paul.kiernan@wsj.com