Lucy Spraggan said she was "gutted" to leave the X Factor because she is not well enough to perform.
The singer pulled out of last weekend's shows and received a free pass to this week. But since she is not well enough to perform this weekend, Lucy said she felt it would be unfair to accept another free pass.
In a statement from the show's organisers, she said: "I am gutted not to be able to continue on this journey but I'm not well enough to perform. To accept another free pass having missed last weekend would not be fair on the others in the competition.
"I wish them all well. I would like to express my thanks to everyone who has supported me. There is no way that this setback will prevent me from fulfilling my ambition. You'll be hearing from me again very soon."
A statement from the X Factor said: "Lucy isn't well enough to perform this weekend so she has decided to withdraw from the competition. We are all sorry to see her go and wish her all the best for the future. She has been a fantastic contestant."
Her mentor, Tulisa Contostavlos, said: "I'm so sorry to lose Lucy from the competition, I have had a brilliant time working with her and I hope I can continue to mentor her in the future. I now count her as a friend as she is an amazing girl."
Show bosses said the singer would continue to receive their "support and care going forward".
Spraggan, 20, writes her own songs and has played guitar for years. She works as a portrait seller in Sheffield. Originally from Buxton, Derbyshire, she performed a song at her audition with lyrics about what happens to her on a night out.
In September, she said: "For a long time in my life, I tried to be whatever everyone else wanted - and as soon as I stopped doing that, things started happening for me."
Spraggan will not be replaced in the competition and one act will leave the show this weekend, organisers said.