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The Canadian singer, who is actually called Claire Boucher, appeared to announce the good news in an uncensored Instagram photo that showed her stomach with the outline of a foetus photoshopped onto it.
Then - thanks to Instagram's rules about showing female nipples - the photo was deleted and replaced with a censored version.
Anyway, in a comment underneath the now-deleted original photograph, Grimes seemed to confirm that she and Musk are to become parents, writing: "I thought about censoring them for a hot minute haha (this may get taken down anyway) but the photo is so much less feral without the nipples.
"Plus being knocked up is a very feral & war-like state of being.
"Might as well be what it is. Plus most of my friends told me not to post them so then I was afflicted w reverse psychology.
"Interrogated my shame on it and decided it was sum weird internalized self hatred to feel uncomfortable abt my body."
As she expected, it did eventually get taken down.
She then posted the censored version of the photograph with the caption: "Censored for insta haha - almost got away [with it]."
While this is Boucher's first child, 48-year-old entrepreneur Musk already has five children, a set of twins and a set of triplets, with his first wife Justine Wilson, who he divorced in 2008.
He has subsequently been married twice to British actor Talulah Riley, before they divorced for the second time in 2016.
Musk, who owns rocket and spacecraft manufacturer SpaceX as well as his electric car and energy company Tesla, is worth a reported $29.2bn (£22.3bn).
He and Grimes have been together since May 2018.
In the caption for her original picture, Grimes made light of the fact that she has been accused of being a gold digger, despite being a successful artist in her own right.
She wrote: "Omg queen of securing elons coin forreal ... #businesswoman."
As you'd probably expect, most of the comments about the announcement have been pretty positive.
One person said: "Yesssss love you"
Another wrote: "You are the Khaleesi queen endboss"
Well, that's the next album name sorted, at least.
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