Szabó was born in Budapest, Hungary. He began playing guitar at the age of 14. In the aftermath of the Hungarian revolution of 1956, he moved to California and later attended the Berklee College of Music in Boston between 1958 and 1960.
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In 1961, Szabó became member of a quintet that was led by Chico Hamilton and included Charles Lloyd,[2] playing what has been described as chamber jazz, with "a moderate avant-gardism.
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The song "Gypsy Queen" from Szabó's debut solo album Spellbinder became a hit for rock guitarist Carlos Santana. During the late 1960s, Szabó worked in a group with guitarist Jimmy Stewart.