Rubinshtein was born into one of Russia's richest families, to Jewish parents in Kharkov, Russian Empire, but grew up in Saint Petersburg. For many years, it was a mystery whether she was born in Kharkiv or Saint Petersburg, complicated by the rumour that "Ida" was short for "Adelaida." Rubinshtein herself would not confirm where she was born, nor if Ida was a nickname, preferring the aura of mystery. Years after her death, the record was discovered in the archives of the Kharkov Choral Synagogue, where her father had been a board member: The birth of a daughter, Ida Lvovna, on 21 September (O.S., N.S. 5 October), to father Lev Ruvimovich, Honorary Citizen of Kharkiv, and mother Ernestina Isaakovna Rubinshtein, had been dutily recorded in the registry for 1883. She had an older sister, Rachel, born in 1876.
Ida's grandfather, Ruvim (Roman) Rubinshtein, had been a successful sugar trader in Kharkov. He moved to Saint Petersburg, where he founded the company, Roman Rubinshtein & Sons, with his two sons, Lev (Leon) and Adolf (Anton). The family multiplied their investment many times over, becoming millionaires by the time Ida was born. The family expanded to own several banks (including the First Bank of Kharkov), sugar mills and breweries.