Elmira Şahtaxtinskaya was born on October 25, 1930, in Baku, Azerbaijan Soviet Socialist Republic, part of Transcaucasian Socialist Federative Soviet Republic, Soviet Union (present-day Baku, Azerbaijan). Elmira grew up in a family, devoted to the national traditions, science, education and service to society. Her mother, Leyla, was a granddaughter of South Azerbaijan ruler, Bahman Mirza Gajar, who moved to Shusha in 1847 and who left behind a huge legacy in diplomacy, geography and history.
Leyla, Elmira's mother, graduated from the Girls' Seminary in Tbilisi and worked as a teacher for some time. Elmira's father, Habibulla Şahtaxtinsky, was a notable Azerbaijani chemist and academic.
Many members of Elmira's family became prominent public figures and left their marks in the scientific, diplomatic, medical and cultural history of Azerbaijan. The Şahtaxtinskys, with their innate intellect and interest in foreign languages, travel, knowledge and public service, operated and lived in France, Germany, Turkey, Iran and Iraq in the 19th and 20th centuries.