In the video, Eilish, 19, is lounging about in bed eating something, at one point giving a goofy smile.
She looks into the camera as she takes a bite of her food and continues chewing, before moving back and casually asking: "Who wants to eat me out?"
Many fans were confused by the weird proposition - although some had an idea why she was trying to get our attention.
One wrote: "DID NOT EXPECT THAT BILLIE."
Someone else said: "Last thing I was expecting to hear."
A third commented: "I was not expecting that ending."
Another said the clip was 'so random', while one other person added: "That definitely caught me off guard."
Someone else, however, reckons they know why Eilish had posted the odd message, writing: "This is an interesting album promotion."
And it would seem as though their theory may be right - with a caption on Eilish's video reminding fans of her album's release date.
"Album out in less than a month," it said.
That's right, Eilish's second album Happier Than Ever drops on 30 July - its release date announced in a recent social media post.
Speaking to Rolling Stone, Eilish explained how the new release - a follow-up to 2019's debut studio album When We All Fall Asleep, Where Do We Go? - was recorded as the world went on pause due to the pandemic, and had been an opportunity for her to dig into her personal trauma.
"I went through some crazy s***, and it really affected me and made me not want to go near anyone ever," she says, but declined to give detail.
Eilish explained that she's letting go of her former self, who would shy away from her emotions to make others feel better, saying: "There've been times where I've been really affected by somebody, and I said to them, 'I need to tell you how you've made me feel'.
"And they said something that was like, 'I can't handle this right now. I just can't handle this right now. This is going to be too much for me'."
As for the album's title, Eilish said: "My mom was saying this yesterday. When you're happier than ever, that doesn't mean you're the happiest that anyone's ever been. It means you're happier than you were before."