Eurythmics Star Dave Stewart's Daughter Kaya Abruptly Leaves 'American Idol'

Kaya Stewart, the daughter of Eurythmics star Dave Stewart, is off "American Idol" -- despite her Rock HOF lineage ... she made a shocking and tearful exit from the competition's Hollywood Week.

Kaya was supposed to perform a duet on Monday night's episode with 22-year-old Fire -- but she stunned just about everyone when she said she was quitting the show because she'd been ill all week.

She broke down as she told the judges -- Katy Perry, Lionel Richie and Luke Bryan -- she'd been unable to fully recover, so she wouldn't be continuing on the show.

Her surprise exit had poor Fire tearing up, but she powered through to sing ... with help from another contestant.

Jayna Elise had been sitting in the audience, and volunteered to duet with Fire ... and they crushed Adam Lambert's hit, "What Do You Want From Me." Fire did most of the vocals and had the judges on their feet, crying for her performance.

As they say ... the show must go on, and Fire did that and then some.

Kaya had been a controversial pick by the judges. Not that she wasn't a good singer, but she auditioned with her superstar father -- who was inducted into the Rock & Roll Hall of Fame alongside Lionel -- playing guitar for her.

It sparked the ol' nepotism, or "nepo baby," conversation again. Haters say her dad's celeb status got her a spot on the show that could have gone to someone else.