Izzet Gayibova was born in Tbilisi, Georgia, in the family of Azerbaijani mufti Jahangir Gayibov and a descendant of the Persian royal dynasty Ziba Qajar (Kadzhar). Through her mother, Gayibova was related to the Belarusian architect Lea Qajar. As a child, Gayibova lived in Istanbul, where her father was a diplomat, attending a French school. The family returned to Tbilisi in 1925, where her father lost his life in the Great Terror of 1937. The rest of the family then moved to Baku, where Gayibova graduated from the university. Gayibova’s fiancee was killed in the Second World War, and she never married and did not have children.

Working in industry, she became the deputy head of the Council of People’s Economy, in the early 1960s founding and heading the Special Artistic-Construction Office (SKhKB), the first office of industrial design in Azerbaijan. While other SKhKB were created in other major Soviet cities (Moscow, Leningrad, Kharkiv, Sverdlovsk, among others), the only one of its kind, the Baku Office focused on the design for the oil industry. It developed over 30 “artistic-construction projects”, including those for electric pipe truck, drill winch, drilling rig, and control rooms. In addition, the Office worked on projects related to automobile, textile, and other industries (products and factory workshops design alike), as well as for the design of domestic consumer objects, such as a series of modular plastic bathroom devices.