Kuznetsov was born in the USSR in Petrovka, a small village in Primorskiy Kray on the Sea of Japan. He graduated from Schukin Theatrical College. Aleksandr Kuznetsov made his first appearance in a movie in 1983. He starred in many Russian movies and TV series. His most known role is Jack Vosmyorkin in Jack Vosmyorkin, The American. Aleksandr Kuznetsov was a key member of the Malaya Bronaya Theater (1985–1989). The actor is working in Russia as well as in United States. He has had television appearances as Nikolai Kossoff in NYPD Blue, as Victor in Crossing Jordan, as Capt. Alex Volkonov in JAG, as Kazimir Shcherbakov in Alias. His most recent performance was the character Ostroff on the thriller series, 24. In 2000 he starred opposite Dolph Lundgren in Agent Red.

С 1976 года по 1982 год учился в МАИ (ФРЭЛА), занимался в театральной студии. В 1985 году окончил Театральное училище имени Б. Щукина. До 1989 года - актер театра на Малой Бронной. С начала 1990-х годов жил в США, с 1993 года снимался в Голливуде (как Alex Kuznetsov, Alex Kuz, Alex Kuzne). В США организовал международную школу актёрского мастерства с методом обучения, основанном на системах К. С. Станиславского и М. А. Чехова. С 2009 года преподавал в школе-студии МХАТ, на русско- и англоязычных курсах. Выступал на сцене Московского Театра киноактера. Основал Московскую международную киношколу «Кузница кино и телевидения».