Mr Musk caused a Twitter storm when he posted last week: “Pronouns suck” Grimes, who has a child with the Tesla CEO, and responded to a since-deleted tweet that said: “I love you but please turn off ur phone or give me a call [sic]. “I cannot support hate. Please stop this. I know this isn’t your heart.”
The meaning behind Mr Musk’s tweet is not know, but he had previously tweeted: “Twitter sucks.”
At the time of writing this original tweet, his previous tweet was still public.
Elon Musk has also caused controversy over the past few weeks by endorsing support for Kanye West’s presidential campaign.
However, a few weeks later he seemed to have a change of heart as the CEO appeared to backtrack after the rapper’s interview with Forbes.
In the interview, West said he was “pro-life” and claimed vaccinations were “the mark of the beast”.
Mr Musk said: “We may have more differences of opinion than I anticipated.”
The couple also announced the birth of their child, X AE A-XII, in May this year.
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Grimes has also made it clear they are not going to “gender them” in case that is not how the child identifies.
She said: “And I don’t want to gender them in case that’s not how they feel in their life.
“I don’t know, I just feel like it doesn’t need to be known.”
Grimes has also had recent success with her latest album, Miss Anthropocene, which was released in February as critics responded in a positive manner.
The 49-year-old CEO of SpaceX admitted that when it comes to caring for their two-month-old baby, Grimes “has a much bigger role than [him] right now.”
Elon Musk said: “Well, babies are just eating and pooping machines, you know? Right now there’s not much I can do.”
He added: “When the kid gets older, there will be more of a role for me.”
He also noted that he intends to use the relationships he has formed with his five older sons as a guide on how to later bond with the newborn.
The newborn baby which he and Grimes have nicknamed ‘X.’
Musk said: “I think just doing what I’ve done with my other kids.”