Ibrahim founded the Jazz Epistles in 1959 with saxophonist Kippie Moeketsi, trumpeter Hugh Masekela, trombonist Jonas Gwanga, bassist Johnny Gertze, and drummer Makaya Ntshoko. Together, they recorded the first full-length jazz album by Black South African musicians. That same year, Ibrahim met jazz vocalist Sathima Bea Benjamin, whom he performed with and eventually married. (The couple have two sons: rapper Jean Grae and pianist Tsakwe. Benjamin died in 2013.)
As apartheid became more entrenched, Ibrahim and Benjamin left South Africa in 1962 for Zurich. In 1963, Benjamin managed to convince Duke Ellington to listen to her husband with his trio, which included Gertze and Ntshoko. That led to a recording session in Paris—Duke Ellington presents the Dollar Brand Trio—and opportunities to perform festivals and on TV and radio. In 1965, Ibrahim and his wife moved to New York, with Ibrahim going on to perform at Carnegie Hall and the Newport Jazz Festival. In 1967, he received a Rockefeller Foundation grant to attend The Juilliard School of Music.