He was born into a Jewish family of traditional musicians. This was founded by his grandfather Levi Babakhan (1873-1926), a minstrel of the last Emir of Bukhara, Alim Khan. Levi Babakhans son Moshe Babakhanov (1910-1983) was also a singer who accompanied himself on tanbur and the frame drum Doira.
Unlike his father and grandfather Ari Babakhanov was a pure instrumentalist. His curriculum aligned with the European musical studies at the Tashkent Conservatory, he graduated in 1958 with the state exam. Due to the Soviet cultural policy, is typical instruments could still be used, but mainly for a European repertoire. Due to the discrepancy between the monophonic and polyphonic Uzbek European music of this constraint led to an artificial cultural hybrids.
Despite his artistic success in Tashkent Ari Babakhanov returned home to Bukhara, where he taught the next 40 years at the music school. There he found with the help of his father and by musicians like Maarufjon Tashpulov, Najmiddin Nasriddinov and Aminjon Ismatov gradually back to Schaschmaqam, the traditional Bukharian music and its evolution made his life's task. By writing down notes and lyrics of classical Persian poetry and folk Uzbek and Tajik poems he contributed to the preservation of this music tradition. He raised a number of lost creations to life that had once belonged to the repertoire of Schaschmaqam. This foundation inspired him to compose his own instrumentals and songs in the traditional style, many of which were popular in Uzbekistan.
In 1991 he founded at the Bukhara State Philharmonic of the first ten people Shashmaqam ensemble, whose members number almost doubled within a few years. After a short time the group performed under the artistic direction Ari Babakhanovs on the Uzbek radio and television, and had established itself in the traditional music scene. In 1998 they released their CD Ari Babakhanov & Ensemble - Shashmaqam: The Tradition of Bukhara in New Samarkand Records.
Since the once large Jewish community of Bukhara has almost dissolved by emigration since the independence of Uzbekistan, Ari Babakhanovs family moved to Germany, where he works with the musicologist Dr. Angelika Jung since 2002 in exploring the Schaschmaqam.