Díaz was born in Buenos Aires, Argentina. Her is father is of Lebanese and her mother is of Spanish descent. Her father was a doctor and her mother was a health care manager. While studying Economics in Buenos Aires in 1996, she took a holiday in Uruguay where she was discovered by a scout from a Milan modeling agency.
After working in Milan for a few years, she was featured in 1999 in the Sports Illustrated Swimsuit Issue, and made the cover of the magazine first in 2002 and again in 2006. On the 2006 cover, she appears with several other models for an "All-Stars" special.