The copyright claim is said to relate to Get Free, from her Lust For Life album.
The American singer tweeted on Sunday: "It's true about the lawsuit.
"Although I know my song wasn't inspired by Creep, Radiohead feel it was and want 100% of the publishing - I offered up to 40 over the last few months but they will only accept 100.
"Their lawyers have been relentless, so we will deal with it in court."
Radiohead themselves were successfully sued over Creep's resemblance to The Hollies' song The Air That I Breathe.
Radiohead had to credit The Air That I Breathe's writers in the notes to their Pablo Honey album and reportedly gave them a cut of the royalties.
Sky News has contacted Radiohead's representatives for comment.
Hear the two songs below: