Tesla shares, down just one percent after Musk's appearance on the Rogan podcast, fell another seven percent in the half hour after Morton's resignation.
Musk replied, "I mean it's legal, right?" before taking a drag.
His departure came as Tesla faces the prospect of a Securities and Exchange Commission investigation into Musk's aborted plan.
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".
"Is that a cigar?" asked Mr Musk when his host first proffered the joint.
The interview took place in California, where both medical and recreational use is allowed, but it is still illegal on the federal level.
The news outraged investors and analysts, as well as the company's board members, who urged Musk to stop posting on Twitter for some time.
"It's like a cup of coffee in reverse", Musk explained.
Asked by Musk whether it was legal to smoke, Rogan assured him that it was, then asked: "How does that work?"
Tesla Inc. (TSLA) shares dropped down to their lowest point in almost six months today amid a lawsuit made by a short-seller who is suing the auto company over claims that they lied to investors about taking TSLA private.
Tesla sank more than 7% in early trading Friday, to $260 per share, after the electric-car maker revealed that its chief accountant, Dave Morton, resigned on September 4. "These things are much more important than creating electric supersonic VTOL", he said.
"I'm not a regular smoker of weed", the Tesla Inc. chief executive officer said late Thursday on the podcast, which was shown live on the internet.