Two people familiar with the company tell CNBC that at least five employees have been fired for circulating a letter that was critical of the CEO.
The open letter was signed by an unknown number of people. According to media reports, the letter was addressed to company executives, and referenced recent sexual misconduct allegations against Musk and described the billionaire's public behavior as a frequent source of distraction and embarrassment.
As of last year, Musk's trust owned almost all of the voting shares of the company.
In an email to employees last month, Shotwell wrote that she believed the allegations to be false and defended Musk.
The New York Times was the first to report the firings. CNBC asked the company for comment, but they didn't immediately reply.