Luft's publicist told People magazine the performer collapsed Friday backstage at her concert at London's Pizza Express Jazz Club and her husband Colin Freeman took her to the hospital.
Freeman informed doctors she lately had been forgetting song lyrics and parts of her monologue from the show, The Hollywood Reporter said.
The 65-year-old breast-cancer survivor underwent tests that revealed she has a brain tumor. She is expected to undergo further exams to determine the severity of her illness and best course of treatment.
The half-sister of singer Liza Minnelli has appeared in the films Grease 2, Where the Boys Are '84, 54 and My Giant, and also was a popular guest star on 1980s TV shows such as Trapper John, M.D. and Murder, She Wrote.