He began studying singing at the Puebla Conservatory at the age of twelve and in 1994 he transferred to the National Conservatory of Mexico City.

From 1997 to 2000 he was a member of both the international San Francisco Adler Fellowship and the Merola Opera Program San Francisco.

In 1997 Alfredo Daza sang Don Giovanni in Mexico City. After moving to the United States, he made his debut in various North American and European opera houses. In 1999 Alfredo Daza sang Schaunard La Bohème at the San Francisco Opera and at the Canadian Opera Company in Toronto.

In 2000 he made his debut as Valentin Faust under Vladimir Jurowski at the Teatro Carlo Felice in Genoa and as Dandini La Cenerentola at the Teatro dell'Opera di Roma. In 2001 Daza sang the title role of Figaro in Rossini's Il barbiere di Siviglia at the Washington Opera, where he interpreted Marcello La Bohème a year later. He was also heard as Marcello at the New York City Opera in a new production of La Bohème, which was broadcast on American television as part of the series Live from Lincoln Center. Alfredo Daza toured Japan with the Michigan Opera Theater as Guglielmo Così fan tutte.

At the Los Angeles Opera he sang Ping Turandot, the barber in Rossini's Il barbiere di Siviglia and in the fall of 2004 the role of Marcello in La Bohème. At the Teatro Giuseppe Verdi in Trieste he appeared as Lescaut in Massenet's Manon. His first Papageno in The Magic Flute followed in Genoa. In the autumn of 2002, Daza made his debut at the Théâtre Royal de la Monnaie in Brussels in the role of Schaunard La Bohème, conducted by Antonio Pappano. In spring 2003 he sang the Papageno Die Zauberflöte in Cagliari. He appeared as Ford Falstaff at the Teatro Comunale di Bologna under the baton of James Conlon and at the Hamburg State Opera under the baton of Simone Young. In summer 2009 he made his Glyndebourne Festival debut as Belcore L'elisir d'amore. In the summer of 2012 he made his debut as Scarpia in Puccini's Tosca at the Kiel Opera. Daza has been a member of the ensemble at the Staatsoper Unter den Linden since 2004.

In 2013 Daza was heard for the first time in an opera by Benjamin Britten: At the Hamburg State Opera he impersonated the role of Sir Robert Cecil in Britten's Gloriana under the direction of Simone Young. In the same year he returned to Los Angeles after a long absence to sing the role of Tadeo Cespedes in the premiere of the opera Dulce Rosa under the baton of Placido Domingo. The baritone is now increasingly specializing in the Verdi roles in his repertoire. He sang Giorgio Germont La traviata for the first time at the Berlin State Opera in 2006, Ford Falstaff in 2007, Posa in Don Carlo in 2008 and since 2009 Renato in Un ballo in maschera under the baton of Phillip Jordan.

He made his debut in February 2014 in the role of Francesco Moor in Verdi's opera I masnadieri at the Konzerthaus Berlin.

In spring 2015, in his native Mexico, he appeared in a Mozart gala (Esto es Mozart) alongside soprano Karen Gardeazabal in the Palacio de Bellas Artes Mexico City. In the same context, he gave a master class for the students of the conservatory. Daza made his debut in 2015 as Valdeburgo/Leopoldo in Vincenzo Bellini's opera La straniera – a concert performance at the Berlin State Opera, in which Edita Gruberova sang the female title role.