Mullodzhanova was born in Dushanbe, Tajikistan to a Bukharian Jewish family. Her father, Itzakhor, was a stage actor, and her mother, Zelpo, originally derived from neighboring Uzbekistan. The Mullodzhanovs trace their ancestry to an aristocratic Levite tribe that has been into performing since the time of the First and Second Temple in Jerusalem.
As a child, Rosa was deeply influenced by her family's passion for performing arts and decided to pursue a career in singing. Her father sent her to the Moscow Conservatory. After graduating cum laude in 1971, Mullodzhanova continued studying opera. She moved back to Dushanbe and sang in numerous theaters. Mullodzhanova became the toast of the opera scene in a very short time. She won one of the biggest awards in the country when she earned the title of "Honored Artist of Tajikistan" ().
In the early 1990s, she and her family immigrated to New York City during the dissolution of the Soviet Union. She settled in Queens, where she lives with her husband and sons and performs in festivals and local shows. Life in New York