Mr. Markell said an investigation could hinder the firm’s bankruptcy advisory practice — whose clients include PG&E, the California utility facing enormous liabilities over wildfire damages — but would most likely not affect other parts of the firm.

“I think McKinsey’s still standing at the end of this,” he said. “It may not be as tall. It may be a bit bowed, but I think they’re still on the playing field.”

The criminal investigation represents a potent threat to a venerable company that has been dogged by mounting criticism that it has prioritized its own profits over clients, ethics and the law. McKinsey refunded millions of dollars in fees after South African authorities accused it of helping associates of the country’s former president, Jacob Zuma, loot public coffers. The firm’s name surfaced in a case federal prosecutors brought against a Ukrainian oligarch because it gave a presentation that cited the need to bribe officials in India. And court records recently revealed its role in helping opioid makers sell more drugs, although the firm was not a defendant in that case.

But the activities of McKinsey’s bankruptcy advising business have invited especially intense scrutiny. Such advisers have significant influence over the handling of bankrupt companies’ assets, and help determine which creditors receive the best returns on defaulted debt.

Much of the criticism has come from Jay Alix, the founder of a competing firm who has attacked McKinsey in courts across the country. He formed an investment company, Mar-Bow Value Partners, to buy debt of bankrupt companies in order to bring complaints against the firm’s restructuring division, McKinsey RTS.

Mr. Alix has told judges he believes that McKinsey does not properly disclose its connections to other parties involved in the cases, breaking rules meant to ensure fair dealing. He has met with mixed results: Judges have voiced concerns about the issues he has raised, but some have dismissed his complaints because they said he lacked standing in the cases.

McKinsey has denied wrongdoing.

“Over the past few years, Jay Alix has waged a relentless campaign based on false allegations to drive McKinsey out of the bankruptcy advisory space in order to advantage his firm AlixPartners,” Mr. Pinkus said. He said courts have dismissed Mr. Alix’s claims in four separate bankruptcy cases, including those of Alpha Natural Resources and SunEdison, as well as a complaint Mr. Alix brought last year under the Racketeer Influenced and Corrupt Organizations Act.