It features a number of artistic-looking strokes running across her shoulders, down her spine and all over her lower back.
The work was completed by tattoo artist Tweakt and was created from a design by Grimes and artist Nusi Quero.
“Don’t have a good pic cuz it hurts too much and I need to sleep,” she wrote to caption the photo of the tattoo. “It’ll be red for a few weeks, but gna be beautiful alien scars.”
On her Instagram stories she showed off the creative process of the design being drawn on a screen before the artist began to work on her back.
Grimes, 33, whose real name is Claire Elise Boucher, is no stranger to tattoos.
She has at least 18 tattoos, some of which she has drawn and completed herself.
Watch: Travis Barker has Kourtney Kardashian's name tattooed on his chest
Grimes’ left hand has a number of Lord of the Rings tattoos, which she got in July 2018. The tattoos are written in the elvish language “Qenya” and match to ones her friend Hana Pestle - aka the musician HANA - has.
She has other matching tattoos - including a Triforce tattoo on her left forearm which matches her brothers’s.
She told Bullett Media in June 2012: "The Legend of Zelda was the first video game me and my brothers ever got, and so we all got matching Triforce tattoos."
Grimes also has the word “Beautiful” tattooed on the back of her left hand.
In an Instagram post, she said about the tattoo: “feeling beautiful despite many imperfections haha, terrible and wonderful memories etched into my skin.
"Even the most screwed up ones were all done w or by my best friends and they all feel like home.”
Perhaps her most striking work - until now - was the brushstroke tattoo on her leg.
It features the Russian word ‘ÑÐ¸Ñ Ð¾’ - roughly translated in to “quiet” in English.
It is the work of tattoo artist Delphine Noiztoy at Love letters tattoo parlor in Los Angeles.
After she got the work in January 2017, Grimes said: "Can’t beat a spontaneous, full-leg tat!"
Some of her tattoos are homemade - including several on her left hand, including a number 8.
She said to : “I did them all myself, I have a Greek meander that is often mistaken for a square wave on my finger (very telling of the times), an alien head because I believe in aliens, an “8” because its my lucky number and a wrist band my friend designed for me that I did in the woods in Minnesota.”
Grimes started dating Musk - the CEO of SpaceX and early stage investor, CEO, and product architect of Tesla - in 2018. The couple announced they were expecting a baby in 2020 - with the star giving birth in May of that year.
Go Won of the South Korean girl group Loona is his godmother.
Elon Musk is worth $167 billion (£121 billion).
Watch: Denise Van Outen gets hypnotised to help relationship