South Korea’s president, Ms. Park, has denied wrongdoing.

Mr. Lee, who goes by Jay Y. Lee in the West, is part of the third generation of the Lee family to lead the conglomerate. While his father was widely seen as old-fashioned, Mr. Lee has been painted by Samsung as equally comfortable in Silicon Valley and in the boardroom, as a leader who could open up the clannish business and reinvigorate Samsung’s flagging reputation for innovation in consumer technology. Samsung is the world’s biggest maker of cellphones.

“Beyond the arrest itself, this is going to be a big blow to the narrative they’ve been building,” said Geoffrey Cain, the author of a coming book on Samsung. “It’s hard to convince shareholders and partners they are a hip Silicon Valley-style company when these charges show them to be a company run like a feudal dynasty.”

Samsung is in effect a collection of widely disparate companies, each with an autonomous, professional management team. Samsung Electronics, the most important of those companies, is broken into high-functioning business units. Because of that, some observers say that the company could continue to run smoothly without Mr. Lee.

Important matters that require Mr. Lee’s imprimatur could be delayed amid the distractions, said Mark Newman, an analyst at Sanford C. Bernstein and Company. “I think that’s the thing you need to worry about: big decisions,” he said.

If executives lower in the hierarchy are implicated, day-to-day operations could become complicated. According to South Korean news reports, other top company leaders have been questioned.

Mr. Lee’s role at Samsung is not necessarily imperiled. South Korea has a long history of pardoning the leaders of its largest family-run companies. Because of Samsung’s size, past efforts to penalize the company or its executives have been met with worries about the effect on South Korea’s economy.

But Mr. Lee’s problems could influence the company’s strategic decisions at a time of major challenges, such as how to bounce back from the debacle over its Galaxy Note 7. A spate of fires last year forced Samsung to recall and then cease production of the phone, tarnishing the company’s name and making it the object of airline safety announcements and jokes on American late-night talk shows.