Aziza was born in Baku to musical parents Vagif and Eliza Mustafa Zadeh

Aziza was born in Baku to musical parents Vagif and Eliza Mustafa Zadeh. Vagif was a pianist and composer, famous for creating mugam-jazz fusion in which his daughter now plays. Eliza is a classically trained singer from Georgia.

They first noticed their daughter's sensitivity to music when she was eight months old. As Aziza recalls the story her mother tells:

“

Once, my father was improvising at the piano playing in the mugam mode known as "Shur," which creates a mood that evokes very deep, sad emotions. As my father was playing, I started to cry. Everyone wondered what was happening to me. Why was I crying? And then mother realized the correlation between my feelings and the music. 'Vagif, please,' she told my father, 'change the scale. Go to Rast. Play Rast.' And he did. Now 'Rast' is characterized by its joyfulness and optimism. And sure enough, with tears still running down my cheeks, I started to make dance-like movements. And Mom pointed out, 'Look, look what she's doing! Change back to Shur!' And when he did, I started crying again louder than before. At least, that's what they tell me. Back to Rast, and I began dancing again.

”

 Aziza enjoyed all forms of art, especially dancing, painting and singing. At the age of three, she made her stage debut with her father, improvising vocals. She began studying classical piano at an early age, showing special interest in the works of famous composers Johann Sebastian Bach and Frédéric Chopin. Soon thereafter, she showed a growing talent for improvisation.

On December 16, 1979, Aziza's father died of a severe heart attack in Tashkent at the age of 39, three days away from Aziza's tenth birthday. (The chronology of important family dates here is very strange. Aziza's birthday is the 19th, her mother's is the 17th. Vagif died on the 16th and was buried on the 18th. Aziza says, "So all those dates-16, 17, 18, and 19-are such a mixture of joy and sadness for us and such a philosophical paradox-life and death juxtaposed upon each other like that.") In order to help her daughter cope with this blow, Aziza's mother gave up her career as a singer to help nurture her daughter's own musical talents.

In 1988, at the age of 18, Aziza's mugam-influenced style helped her win third place together with American Matt Cooper in the Thelonious Monk piano competition in Washington, D.C. It was around this time that she moved to Germany with her mother.

Aziza released her debut album, Aziza Mustafa Zadeh, in 1991. Her second album, Always, won her the Phono Academy Prize, a prestigious German music award, and the Echo Prize from Sony. She has since performed in many countries with many jazz and traditional luminaries and released several more albums, the most recent being Contrasts II, released in 2007.