Tesla Inc., with a fresh civil fraud settlement now behind it, faces a new legal problem: a deepening criminal investigation.

Federal Bureau of Investigation agents are examining whether Tesla misstated information about production of its Model 3 sedans and misled investors about the company’s business going back to early 2017, people familiar with the matter say.

Action in the criminal investigation, headed by the U.S. attorney’s office in San Francisco, has intensified in recent weeks after the Securities and Exchange Commission settled separate civil charges with Tesla and Chief Executive Officer Elon Musk, the people said.

Tesla had disclosed on Sept. 18 that it had received a request for documents from the Justice Department, 10 days before the company and Mr. Musk struck a settlement with the SEC over civil charges in a separate case involving controversial tweets from Mr. Musk.

But it hasn’t been previously reported that the Justice Department is focusing on Tesla’s Model 3 production issues dating to early last year and that the criminal securities-fraud probe is intensifying.