Calle has put together a 37-track collection memorialising her late feline, Souris, a name which means mouse in English.
The album opens with "Message to Souris" by Bono, which he recorded via voicemail.
"She seems to hide all looks that have ever fallen into her," the U2 frontman sings. "So that like an audience she can look them over. Menacing and sullen, curls asleep with them. Then all at once, as if awakened. She turns her face to yours. And with a shock, you see yourself. Tiny, inside the golden amber of her eyeballs."
Jarvis Cocker, The National, Laurie Anderson, and Casey Spooner have also contributed songs to the album, titled "Souris Calle".
The artist lost her beloved cat in 2014, the same year her father passed away. In June, she announced she was creating a tribute exhibition, which opened in October. It features photographs and writings about the deaths of Calle's cat, family members and friends.
In an interview with German website Artnet, the conceptual artist said that she hoped her latest project would highlight the extent of the grief she felt at the death of her pet.
"When you say you're sad about the cat, it's a bit obscene for people," she explained. "You can't say that. I mean, if I say my mother or my father is dead, everyone tells me 'Oh, poor thing, she lost her mother, oh, poor thing, she lost her father,' but if we say that about our cat, we seem ridiculous. It makes me laugh, when for me, in my daily life, it was almost more violent, because I lived with my cat. I didn't live with my parents."