The two men also drank whiskey during the interview, and Musk pointed out that alcohol is also a drug.
"Assuming that the South African-born businessman would not accept, the podcast host asked: "'You probably can't do this because of stockholders, right?"
"I mean it's legal, right?", Musk responded, as he accepted the joint and took a puff.
Musk has said the company is producing more than 5,000 Model 3 electric cars per week, and cash generated from the sales will bring sustained quarterly profits.
Earlier in the day, Reuters reported the prominent short-seller Andrew Left has sued Tesla and Musk, saying Musk fraudulently engineered his since-abandoned plan to take Tesla private to "burn" investors hoping the electric auto company's stock price would fall. Tesla noted in a statement to Reuters that Morton opted to depart from the company due to his discomfort with the level of public attention and Tesla's overall pace of work.
Tesla chief executive Elon Musk at a news conference on February 6.
Tesla shares fell as much as 10% to $252.25 as of 9.46am in NY, the steepest intra-day drop since June 2016.
Tesla's top accountant has quit less than a month into the job and the company's human resources chief is also set to depart, adding further to the electric carmaker's troubles.
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The exchange lasted more than five minutes - with an interruption from Sen. "We shouldn't have to put up with this kind of stuff". The Capitol Police can't close the room to the public and can't keep out people who look like they might disrupt the hearing.
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It's actually a quite profound and interesting (despite Musk smoking dagga being the hook that got you here - go to 2:10:15 for that).
Marijuana is legal for medical and recreational use in California, where the interview took place.
At one point, Musk and Rogan shared a spliff, though Musk said doesn't make a habit of smoking weed, which he called "a cup of coffee in reverse". "As a result, this caused me to reconsider my future", Morton was quoted as saying in a company filing.
Tesla was not immediately available for comment.
Speaking of the what lies ahead, Musk said being forever constrained to Earth "would not be a good future".
"I don't think you would necessarily want to be me; you wouldn't like it that much", Musk quipped.
"Electric cars are important, solar energy is important, stationary storage of energy is important".
Meanwhile, shareholder activist and short-seller Andrew E. Left sued Tesla and Musk on Thursday, alleging that Musk "artificially manipulated the price of Tesla securities with objectively false tweets in order to "burn" the Company's short-sellers".