Malayev was born in the city of Mary, (today in Turkmenistan) to a Bukharian Jewish family and raised in the town of Katta-Kurgan.

He learned to play the tar and the tanbur (both lute-like instruments), as well as the violin, and immersed himself in the shashmaqam genre.

[1] In 1994, following the breakup of the Soviet Union, Malayev emigrated to the United States where he settled in Queens, New York City along with thousands of other Bukharian Jews.

Although it was a considerable step down from his fame and popularity in Uzbekistan, Malayev emigrated as he was unable to have his poetry published in his homeland, a restriction he suspected was due to either anti-Semitism or the state of the cultural bureaucracy.

[1] On May 29, 2011, in Queens, NY, USA, an honorary concert celebrating Ilyas' 75th year in his memory was held where various Bukharian Jewish and Uzbek performers gave tribute to the virtuoso.