The singer, whose album Sun was released in August following a six-year hiatus, took to Instagram to share news with her followers.
The star, whose real name is Chan Marshall, revealed she has been suffering from angioedema - a condition which causes sudden swelling - and facing financial difficulties.
Marshall wrote: "I may have to cancel my European tour due to bankruptcy and my health struggle with angioedema.
"I have not thrown in any towel, I am trying to figure out what best I can do. Heart broken. Worked so hard. Got sick day after Sun came out and been struggling to keep all points of me in equilibrium: mind, spirit, body healthy centered and grounded."
She added: "I am doing the best I can. I f**king love this planet. I refuse to give up. Though I may need to restrategise for my security and health."
Cat Power is currently scheduled to play dates throughout continental Europe in December, before reaching the UK for a show at London's Roundhouse on December 12.
Marshall was previously in a six-year relationship with Giovanni Ribisi before the pair split earlier this year. The actor subsequently married model Agyness Deyn in a surprise ceremony in June.
Watch the announcement of Cat Power's album Sun below:
> Cat Power announces new album 'Sun', free download 'Ruin'