The punk icon - real name Marian Joan Elliott-Said - revealed she is battling the illness on her website and is currently undergoing treatment.
A statement posted on Poly-styrene.com read: "It comes as a huge shock to all those who know PolyStyrene and X-raySpex that Poly has been diagnosed with cancer, she is currently undergoing various treatments in her battle with this illness.
"She is devastated that she cannot commit to any live dates at this stage, but her album remains a very positive force in her current journey."
Poly is releasing a new solo LP, `Generation Indigo`, at the end of March.
She also revealed her illness to her fans via her twitter page, writing: "It`s been a bit of a battle fighting this cancer but hey ho I`m still alive, Luv Poly x (sic)"
The 53-year-old musician and her band X-RaySpex were at the forefront of the punk rock scene in Britain in the late 70s and their album эGerm Free Adolescents` is considered one of the most important records of the movement.
The `Oh Bondage, Up Yours!` singer has been cited as an influence to several modern female-led rock groups, including the Yeah Yeahs Yeahs and The Gossip.