"[This is] the behavior of a man who should not be running a public company," Cramer said on "Squawk on the Street."
Late Thursday night, Musk smoked weed and drank whiskey during an interview on comedian Joe Rogan's podcast.
Cramer said the morning after, "I don't think anyone should be in a situation where there are companies completely under a cloud, where he is completely under a cloud and he does something that I regard as being unstable."
Tesla did not immediately respond to CNBC's request for comment on Cramer's remarks.
Shares of Tesla were sharply lower Friday after more bad news in the form of two high-level executive departures, including Dave Morton, the company's chief accounting officer, who was only on the job for a month.
Cramer said Morton's quick resignation Friday morning was "such a red flag."
Tesla stock, down as much as 10 percent in early trading, was now on pace for worst day since June 22, 2016, when it lost nearly 10.5 percent.
Tesla started to garner lots of negative attention after Musk's tweet last month about possibly taking the electric car maker private stunned Wall Street and Washington regulators. The take-private idea has since been abandoned.
At the time, Cramer urged investors to listen to comments by billionaire investor Mark Cuban on CNBC who defended Musk. Cuban said, in part, "When you invest in an entrepreneur, you get the personality."
"We keep expecting a certain level of convention, and [Musk's] not going to give it to you," Cramer, host of "Mad Money" said in August. "Therefore, you should stop looking for it."
Musk had been acting erratically for months even before the take-private tweet and the subsequently bizarre interviews with The New York Times and Rogan.
In May, Musk rudely cut off analysts on Tesla's first-quarter earnings call, something he apologized for on the second-quarter call in August.
Musk was also launching tweetstorm after tweetstorm all summer long as he was dealing with production problems for the automaker's new, less expensive sedan, the Model 3.