Haber was born in Bologna in a Jewish family of mixed ancestry (his father was a Romanian Jew and his mother Italian) and spent his childhood in Israel.

[6][7] He is also a distinguished theatre actor, having performed amongst others in Orgia by Pier Paolo Pasolini, Woyzeck by Georg Büchner, The Miser by Molière, Uncle Vanya by Anton Chekhov, Dialogo by Natalia Ginzburg and A Servant of Two Masters by Carlo Goldoni.

He has been touring theatres since 2006 with Tango d'amore e di coltelli, with music by Ástor Piazzolla, based on a text by Jorge Luis Borges.

[9] As a singer, he has released three albums: Haberrante, Qualcosa da dichiarare and Il sogno di un uomo.

In June 2011 Haber attempted to kiss actress Lucia Lavia onstage during a rehearsal for Othello at the Teatro Romano di Verona.