'2012 (You Must Be Upgraded)' was recorded as part of The Flaming Lips' Heady Fwends project.
"It's exactly what people would think a Ke$ha/ Flaming Lips track would sound like," Flaming Lips frontman Wayne Coyne said of the song via Facebook.
"It's obnoxious and funny. That's why we like it so much - she wasn't precious about the whole thing."
He added: "She was really into this idea of doing a song about the year 2012 and doomsday and what's going to happen.
"She sent me the most primitive f**king s**tty 40-second demo, and we took that and ran with it.
"Her section of the song is very optimistic - she's singing about the end of the world, but she's also on ten hits of acid, so she's having a good time - and my section is completely f**ked up."
Other songs on the 13-track Heady Fwends double-vinyl, which was released on Saturday as a limited edition for Record Store Day, were collaborations with Bon Iver, Yoko Ono, Nick Cave, Erykah Badu and Chris Martin, among others.
> Ke$ha, Flaming Lips recording 'song about futuristic sex toys'
Watch the making-of video for The Flaming Lips and Ke$ha's track below, featuring snippets of other collaborations between the artists: