White, 30, died of an apparent suicide on Monday night in Los Angeles.
Zelda Williams tweeted, "Heartbroken to continue to watch sweet, kind souls be consumed by darkness. May it never hurt less, so we never grow numb to the loss."
She added, "In honour of @littleirishcat, please check out pieta.ie. They do great work in her wonderful home country. RIP Cat." Pieta House is a suicide-prevention center in Cathriona's native Ireland.
The death hit close to home for Zelda, who lost her famous father when he committed suicide at the age of 63 last year.