Dalla was born in Bologna, Italy. He began to play the clarinet at an early age, in a jazz band in Bologna, and became a member of a local jazz band called Rheno Dixieland Band, together with future film director Pupi Avati. Avati said that he decided to leave the band after feeling overwhelmed by Dalla's talent. He also acknowledged that his film, Ma quando arrivano le ragazze? (2005), was inspired by his friendship with Dalla.