Japanese prosecutors jailed Carlos Ghosn, an auto industry titan and one of the world’s best-known business executives, accusing him of underreporting his pay—and setting off a leadership crisis at the globe-spanning auto alliance he forged.

Nissan Motor Co. , where Mr. Ghosn serves as chairman, said Monday that it went to the authorities with details of an internal probe that alleged he incorrectly reported his compensation in filings over many years. The Japanese auto maker also said it would seek to oust Mr. Ghosn from his position.

Almost two decades ago, Mr. Ghosn was handed the job of creating what would become an unusually deep industrial partnership between France’s Renault SA and Japan’s Nissan, which at the time was struggling financially. He later added Mitsubishi Motor Co. , also of Japan, turning three relatively small players into a colossus that now makes more cars than any other manufacturer besides Volkswagen AG . Amid recent strains between partners and a fast-changing auto industry, Mr. Ghosn was the glue keeping the alliance together.

The arrest also threatens one of the most-storied reputations in the modern auto industry. From Detroit to Tokyo, the 64-year-old businessman has won admirers—and critics—for the sometimes-deep cost cutting and layoffs he pushed at the automotive operations he led.

In France, he earned the nickname “le cost killer.” A comic book about his life was popular in Japan. In recent years, though, Mr. Ghosn has faced criticism for his lack of succession planning and for his high remuneration. In Japan, his legacy more recently has been dented by quality-control issues.