According to two sources familiar with SpaceX and an internal email sent by President and COO Gwynne Shotwell, SpaceX has fired at most five employees involved in spreading a letter that criticized CEO Elon Musk.

According to CNBC's copies of the email, Shotwell stated that the company had "terminated a few employees involved" and called "blanketing many thousands of people in the company with repeated unwelcome emails" unacceptable. The Verge first reported that the open letter was circulated by SpaceX employees and signed earlier in the week.

Shotwell wrote, "we have too much critical work and no need to engage in this kind of activism." He also stated that the letter had "upset many" and "made employees feel uncomfortable and intimidated."

According to media reports, the letter addressed company executives and described SpaceX employees' public behavior as "a frequent source of distraction and embarrassment."

The firings of SpaceX were first reported by the New York Times. CNBC reached out to SpaceX for comment but did not respond immediately.

Musk is the majority shareholder in the privately-held company. His trust holds 78% of SpaceX voting shares.

Musk has a quirky persona, especially on Twitter, where he provides commentary and updates about SpaceX and Tesla's electric vehicle company.

Musk stated that he uses Twitter for self-expression and compared his service use to the way "some people do their hair." He is looking to buy a social media company.

Musk stated that freedom of speech was crucial to Twitter users during a Thursday all-hands meeting. This is true even if the company is privately owned, such as SpaceX.

Business Insider reported last month that there were recent allegations of sexual misconduct against Musk in an internal SpaceX letter.

According to the report, Musk sexually harassed an employee on a SpaceX private flight and paid $250,000 for her silence.

After the misconduct allegations, Shotwell wrote in an email to employees that she was standing by Musk and said she believed the allegations were false.

Shotwell wrote Thursday that SpaceX's leadership was "more dedicated to ensuring we maintain a great, ever-improving workplace than any other I have seen."

Shotwell also stressed that SpaceX has three launches planned for this weekend "within 37 hours" and ongoing support to the International Space Station.

Shotwell stated, "I am sorry for the distraction." "Please keep your eyes on SpaceX and make the most of your work time."