Of 50 United States sates, recreational cannabis remains illegal in 41 - but it was legalised in California, where the podcast was filmed, in January.
Tesla did not immediately respond to ABC News' request for comment.
Shares of Tesla fell Friday morning.
A screengrab of Tesla boss Elon Musk smoking marijuana.
Toward the end of the more than two-hour interview that was live-streamed on YouTube, Mr. Rogan pulled out a joint that he described as marijuana wrapped inside tobacco.
Elon Musk has added another bit of freakish behaviour to the list by smoking a joint during a live interview.
His departure came as Tesla faces the prospect of a Securities and Exchange Commission investigation into Musk's aborted plan.
During the show, Musk said he "almost never" smoked.
"It's legal right?" Musk asked, before Rogan said it was "totally legal" and the entrepreneur took a drag of the cigarette.
Company updates and news reports in the weeks that followed poked holes in Musk's proposal, though, and Tesla formally called off the take-private talks in late August .
Musk did not directly address the suit during the Rogan sit-down.
The 47-year-old billionaire later said he wasn't a "regular smoker" of marijuana because he doesn't find it "very good for productivity".
Long a polarising figure because of his swashbuckling style, Musk's champions see him as an entrepreneurial genius with the potential to remake the transportation system, while his detractors see him as an egotistical blowhard whose outsized promises have driven unjustified gains in the company's values.
Even before Musk's surprise August 7 tweet that he had funding "secured" for a go-private deal, Tesla had been under scrutiny from investors, analysts and short-sellers as it works to hit production targets and slow its cash burn.