Shares fell about 7pc as trading opened on Friday.
But it was the puff of smoke that got the headlines.
Rogan told Musk he'd rolled marijuana in tobacco leaves.
"So is that a joint?" "I don't think people would like it that much".
He told Rogan he thinks that merging humans with computers is the approach that "seems probably the best for us: if you can't beat it, join it".
"I mean it's legal, right?" asked Musk.
During the interview, the pair discussed Musk's ability to dream up ideas and inventions, with the billionaire comparing the way his brain works to a "mutation", saying when he was a child he thought he was "insane". Mr. Musk asked before taking a hit. Then the conversation morphed into the science-fiction side of autonomous cars.
Minutes later the phone in Musk's pocket began sending out alerts.
"You getting text messages from chicks?" He added that he "almost never" smoked marijuana. I don't find that it's very good for productivity.
The aura of weed has surrounded Musk before.
Morton's brief tenure with the company coincided with the aborted go-private push. The price dipped as low as $254.02 before rebounding to the $260-$270 range at midday.
Now, with the company set on staying public, its finances are under extreme scrutiny from investors and analysts as it fights to become profitable.
Chief accounting officer Dave Morton gave notice on Tuesday that he was resigning less than a month into the job, according to a filing.
The chief accounting officer has left less than a month after joining, while its HR officer is also reported to have resigned a year after joining.
The appearance was the latest unorthodox move by Musk, who has often surprised investors with brash and unpredictable behavior as Tesla has sought to live up to lofty manufacturing targets for its Model 3 electric vehicle.