Su Young Boudreau, 41, walked into restricted sections of the Texas facility on Tuesday, falsely telling employees “I am the wife of Elon Musk”, according to authorities.
Cameron County Sheriff’s Office was alerted to the incident and responded to the scene to arrest Ms Boudreau on suspicion of criminal trespass.
A statement on Wednesday, shared on Facebook, said: “As per the security personnel, a female was found wandering inside an only employees building, she was asked to identify herself and she claimed to be the wife of Elon Musk.
“In the course of the investigation, deputies discovered that Boudreau was not affiliated to Space X Industries, surveillance footage was obtained to corroborate the initial statements and it was confirmed that she was not the wife of Elon Musk.”
The statement added: “Boudreau insisted she was heading home to her husband, Mr Musk.”
Ms Boudreau was transported to and booked into the nearby Carrizalez-Rucker Detention centre without further incident.
The sheriff’s office said that a police report was then filed on 25 September and Ms Boudreau was warned to stay away from Space X.
A mug shot of Ms Boudreau showed the woman with her eyes closed and inflammation around her left eye.
It is unclear if this was sustained during her arrest.
It is unknown what, if any, connection she has to Mr Musk or if she is a fan of the tech entrepreneur.
The 52-year-old billionaire owner of Tesla has been married three times – to Justine Wilson from 2000 to 2008 and twice to Talulah Riley, from 2010 to 2012 and then from 2013 to 2013.
He was also in a well-reported relationship with the singer Grimes from 2018 to 2021.
He has had 11 children with different partners, although one has now died.
“Having children is saving the world,” Mr Musk tweeted on September 25, pinning this message to his page.
Mr Musk has not commented about the trespass incident on X, but instead used the site on Tuesday to share a meme of other social networks apparently obeying his orders.