Kuinova was born in Samarqand, Uzbek SSR, but moved to Stalinabad, Tajik SSR with her seven brothers and two sisters when she was thirteen years old, after their father was jailed and murdered by the Soviet government for his mercantile prosperity. Her family were Bukharian Jews, and their last name was originally Cohen, but Fatima changed it to Kuinova to escape the persecution Jews faced under Stalin.[dubious ] During her childhood, she knew the famous Mullodzhanov family and was a friend to Shoista Mullojonova. Fatima was raised in Central Asia under Stalin's Soviet regime and spoke Russian, but she also learned Bukhori, which is a dialect of the Persian Tajiki language. Her father was the cantor of the Bukharian Jewish synagogue and taught Fatima the music of her Bukharian Jewish heritage. Kuinova began singing in different festivals at a young age.[clarification needed] She also sang for Joseph Stalin, who was ignorant of her Jewish faith.[dubious ]
Fatima became famous after performing for the soldiers during World War II. In 1948, she was named "Honored Artist of the Soviet Union". After that, she began to study Shashmakom music and sang it throughout the Soviet Union and Central Asia. Kuinova became the lead singer of the Tajik State Philharmonic, with long-time friend Shoista Mullojonova. The two were widely recognized in the republic and were some of the Soviet Union's leading traditional performers. Both Fatima and Shoista were soloists in the Tajik Ensemble "Rubobistok" that performed on television and radio throughout the Tajik SSR, Central Asia and the USSR and traveled to sing in areas like Kiev, Leningrad, and Moscow. She also went on tours to Europe, Afghanistan, and Iran, where she sang for the Shah.
She immigrated to Queens, New York, USA in 1980 and settled in Rego Park, where she founded and was the lead vocalist for the Shashmaqom Music of the Bukharan Jews Ensemble. In 1992, Kuinova was a recipient of the National Heritage Fellowship award, given by the National Endowment for the Arts. In Queens, Fatima works with the Bukharian Jewish musical community and performs in numerous cultural and folk events in New York City.