She was born in Cienfuegos, Cuba to Ricardo Alonso and Conchita Bustillo. She moved to Venezuela with her parents when she was 5 years old. She took her first steps in show business when she crowned Miss Teenager Of The World in 1971 and was the runner-up of the Miss Venezuela pageant in 1975; thereafter she quickly became a popular actress in Venezuela.

Alonso became the front woman of the band Ambar in 1979, and started a very successful career as a solo recording artist in 1982, with the release of "Dangerous Rhythm". As her two albums with Ambar and her solo debut were recorded in English, it was her sophomore album "Maria Conchita" from 1984 that made her a singing superstar in the Spanish-speaking market, receiving a "Best Latin Artist" Grammy nomination for it in 1985. She made her Hollywood film debut in 1984 in Moscow on the Hudson with Robin Williams, and also appeared in movies like The Running Man, Predator 2, The House Of Spirits, Colors and the TV reality show I'm a Celebrity, Get Me Out of Here!. She also became the first Latin-born actress to star in a Broadway show in 1995, playing Aurora in Kiss Of The Spider Woman. Alonso also acted in the romantic comedy called The Last Guy on Earth (2006) (post production). Alonso posed for a non-nude but sexy pictorial in the December 1991 issue of the Mexican edition of Playboy. Alonso was casted to play the mother of Gabrielle Solis, Lucia on the ABC hit show Desperate Housewives the episode aired February 19, 2006. She is also starring in the live-action film of the comic book, El Muerto, as Sister Rosa.