Ohanessian was born in Baghdad in 1927 to a well-to-do Armenian family. Her father, born in Persia, had settled in Baghdad after a time in India working with the British. Her mother and two uncles were orphaned survivors of the Armenian genocide. Both parents encouraged her to study music. Ohanessian enrolled in the Institute of Fine Arts, graduating with special mention as a piano major. Upon graduating, she served as an assistant to her Romanian piano professor, Julien Hertz. An Iraqi governmental scholarship allowed her to further her studies at the Royal Academy of Music in London with professor Max Pirani. Four years later, she received her LRAM in piano performance and pedagogy, and a second major in singing. She went on to receive a Fulbright Scholarship to study at the Juilliard School in New York City, which culminated in a debut performance at Carnegie Hall. Her scholarship was then extended for another year, due to the 14 July Revolution in Iraq.