It was initially reported that five employees were let go by the rocket company following the letter, but now that number has been increased to nine, workers and their lawyers told the newspaper.
Charges alleging unfair labour practices were reportedly filed with the National Labor Relations Board by eight of the nine employees on Wednesday.
The group alleges that it was illegal for the California-based company to fire the workers over the letter, says the newspaper.
The letter was circulated earlier this year after Mr Musk tweeted a joke about a May report that SpaceX had settled a sexual harassment claim made against him.
“Elon’s behavior in the public sphere is a frequent source of distraction and embarrassment for us, particularly in recent weeks,” the employees wrote in the letter, which the newspaper obtained in June.
It went on to demand that the company “separate itself from Elon’s personal brand” and for Space X to clarify that his online behavior “does not reflect our work, our mission, or our values.”
Two SpaceX employees told the newspaper that the day after the sackings the company held a meeting for 20 SpaceX engineers, where vice-president Jon Edwards confirmed the employees had been fired for criticising Mr Musk.
“SpaceX is Elon and Elon is SpaceX,” Mr Edwards reportedly told the meeting.
Meanwhile, Twitter has fired “dozens” of employees over critical comments they made about new owner Mr Musk on the company’s internal Slack channel, according to ABC News.
“We regret to inform you that your employment is terminated effective immediately,” read an email from Twitter HR to some employees earlier this week.
“Your recent behaviour has violated company policy.”
The Independent has requested comment from SpaceX.