CNBC has learned that Musk was defended by Shotwell in an email to employees last week.
I believe the allegations to be false because I have worked closely with him for 20 years and have never heard anything similar, Shotwell wrote in a company-wide email.
Musk denied the allegations that he propositioned a flight attendant on one of his private jets. Musk told Business Insider that there is a lot more to the story, and that the flight attendant was paid $250,000 in severance after confronting the company.
Shotwell emphasized in her email that she will never comment on any legal matters involving employment issues, before noting that Musk denied the allegations as "utterly untrue".
Shotwell noted that the company has a zero tolerance policy for harassment and that every accusation is taken seriously and investigated.
CNBC requested comment on Shotwell's email, but the company did not reply immediately.
SpaceX President and COO Gwynne Shotwell