Mr Morton - who joined only one month ago - said he was resigning because "the level of public attention placed on the company, as well as the pace within the company, have exceeded my expectations".
His departure came as Tesla faces the prospect of a Securities and Exchange Commission investigation into Musk's aborted plan.
"I can not answer questions about potential future products".
Elon Musk found himself in the middle of another controversy on Friday, after he smoked weed and sipped whiskey during a rather odd Thursday night podcast hosted by comedian Joe Rogan - with some suggesting the eccentric billionaire had acted irresponsibly.
And yes, Musk took a puff of what's been described as a joint of tobacco mixed with marijauna, which is legal in California. Musk works so many hours that employees have found him sleeping under tables at Tesla's facilities, they say. "I don't actually notice any effect ..."
The tech entrepreneur continued by assuring viewers that he is "not a regular smoker of weed", since it's not "very good for productivity".
Trump wants investigation into anonymous New York Times opinion piece
Citing company policy, Ha refused to comment on whether the Times received any substantial threats to its office or employees. "We're going to take a look at what he had, what he gave, what he's talking about, also where he is right now", he said .
Musk also serves as CEO of SpaceX, an aerospace manufacturer that is a contractor for the U.S. Air Force.
Musk stunned investors last month with tweets saying he had funding to take the company private for $420 (£323) a share. Friday was also the last day for Sarah O'Brien, Tesla's vice president of communications, who announced her resignation last month.
"We have been calling for a Co-CEO or COO to assist to codifying the leadership structure and in so doing, the culture at Tesla".
"We think this is further evidence that the time is now for management and the board to address these issues", he added.
On Friday, Tesla shares dropped to almost $252 - their biggest single-day drop in two years after Musk was seen smoking weed on the show.
Tesla will stay public, Musk said on August 24, ending more than two weeks of speculation and calculation about how much a go-private deal would cost and who could be involved in it. While there is no sign of such a move, Tesla released a long list of executive appointments late Friday, including that of Jerome Guillen, an eight-year Tesla veteran with experience at the German automaker Daimler, to oversee all automotive operations.
Tesla said cash from Model 3 sales will pay the bills and drive profits.
Especially weird moments involving the Tesla chief of late include disparaging remarks about a Briton who helped save boys trapped in a cave in Thailand and the abrupt shutdown of Wall Street analyst questions during a contentious earnings conference call this spring.