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Babadzhanian was born into an impoverished Armenian family in the village of Chardakhlu near Yelizavetpol (later Kirovabad, now Ganja, Azerbaijan), then part of the Russian Empire. Ivan Bagramyan, a fellow Armenian who would also go on to become a Marshal of the Soviet Union, was born in the same village. Babadzhanian attended the local, four-year primary school in Çardaqlı before moving to Tiflis (Tbilisi) in 1915 to continue his education at an Armenian secondary school there. His family, however, was unable to support him financially for long and he was forced to return to home, where he went to work in the fields.