News of the probe comes more than five months after CNN Business reported that Tenev, the public face of Robinhood, is not registered with FINRA, short for the Financial Industry Regulatory Authority. That's despite the fact that he presides over one of the nation's largest and most powerful online brokerages.

It also comes on the eve of a blockbuster initial public offering that could value Robinhood at $35 billion.

In a filing late Tuesday, Robinhood said it received a FINRA investigative request seeking documents and information related to its compliance with the agency's registration requirements for member personnel.

Robinhood said the FINRA investigation is related to the "non-registration status" of both Tenev and co-founder Baiju Bhatt, who now serves as chief creative officer.

"Robinhood is evaluating this matter and intends to cooperate with the investigation," the company said in the filing.

FINRA declined to comment on the matter, noting that its investigations are confidential. Robinhood did not respond to a request for comment.

Robinhood is expected to price its IPO on Wednesday and begin trading on the Nasdaq the following morning, CNN Business previously reported.

"Robinhood is facing lots of scrutiny in the run up to its IPO, and regulators are poring through its operations and structure," James Tierney, an assistant professor of law at the University of Nebraska College of Law, said in an email.

Tierney, who previously worked at the SEC on FINRA registration matters, said it's not surprising this scrutiny "extends to Tenev's registration status, given his prominent role as the public face" of the company.

Should Tenev be FINRA-registered?

The FINRA investigation comes after Senator Elizabeth Warren, in a February statement to CNN Business, called on regulators to examine whether executives like Tenev "should be licensed and trained on market rules and risks."

FINRA generally requires that the CEOs of registered broker-dealers be registered with the agency. The aim is to make sure these executives receive compliance training and demonstrate the competence required for leadership roles. Being registered with FINRA also allows the public to track any violations by licensed individuals via the agency's Broker Check tool.

Tenev is the CEO of Robinhood Markets, the parent company that is not registered with FINRA. (Robinhood Markets owns a broker-dealer and a clearing broker.)

The CEO of a parent company that owns a broker-dealer does not necessarily need to be registered.

At the time of the initial CNN report, Robinhood told CNN Business that Tenev does not directly oversee the FINRA-registered managers of the broker-dealer or the clearing broker, but declined to say who does.

Some experts expressed alarm at the fact that Tenev is not registered with FINRA, while others said it may not be a problem.

Latest run-in with FINRA

Some of Robinhood's rivals do have CEOs with FINRA licenses, while others do not. For instance, the CEOs of Charles Schwab (SCHW) and Robinhood rival Webull are registered with FINRA and have their Series 24 licenses as principals.

However, Square (SQ) CEO Jack Dorsey is not listed as being registered with FINRA. (In addition to its payment platform, Square's Cash App lets users invest in bitcoin and individual stocks).

The key may be just how involved Tenev is with Robinhood's day-to-day operations. Some of Tenev's prior comments suggest he holds a significant managerial role, including being involved in delicate negotiations with its clearinghouse during the GameStop trading turmoil in January.

In a late February letter to Sen. Warren, FINRA said that these determinations are "fact-specific" and require "careful assessment of the individual's activities."

The FINRA licensing investigation is just Robinhood's latest run-in with the regulator.

Last month, FINRA slapped the brokerage with its biggest-ever penalty and accused the company of harming millions of customers and giving investors "false or misleading information."

Robinhood neither admitted to nor denied the charges.