Arturo Márquez was born in Alamos, Sonora, Mexico in 1950. He began his musical training in La Puente, California in 1966, later studying piano and music theory at the Conservatory of Music of Mexico and composition at the Taller de Composición of the Institute of Fine Arts of Mexico with such composers as Joaquín Gutiérrez Heras, Hector Quintanar, and Federico Ibarra. He also studied in Paris privately with Jacques Castérède, and at the California Institute of the Arts with Morton Subotnick, Stephen Mosko, Mel Powell, and James Newton. In recent years, Marquez has written a series of danzons, works based on an elegant Cuban dance that migrated to Veracruz, Mexico.  His Danzon No. 2 is among the most popular Latin American works to emerge since the 1950s.   In February 2006, Arturo Marquez received the "Medalla de Oro de Bellas Artes" (Gold Medal of Fine Arts), the highest honor given to artists by Mexico's Bellas Artes. That evening the concert #El Danzon según Márquez" (The Danzón according to Márquez) was presented at the Palacio de Bellas Artes. The concert included six danzons, all contained on a forthcoming CD.

Márquez has received commissions from the OAS, the Universidad Metropolitana de Mexico, the Universidad Nacional Autónoma de Mexico, Festival Cervantino, Festival del Caribe, Festival de la Ciudad de Mexico, and the Rockefeller Foundation. He has received grants from the Institute of Fine Arts of Mexico, the French Government, and the Fulbright Foundation. In 1994 he received the composition scholarship of Mexico's Consejo Nacional para la Cultura y las Artes. Márquez's Octeto Malandro (Misbehaving Octet) was commissioned and premiered by Philadelphia's Relâche Ensemble in 1996, and subsequently recorded by Relâche for Monroe St. Records. Márquez's flute concerto, commissioned by the Rockefeller Foundation and the Consejo Nacional para las Artes, was premiered by James Newton. Other works by Márquez include En Clave for piano, Son a Tamayo for harp, percussion, and tape (featured at the 1996 World Harp Congress), Homenaje a Gismonti for string quartet, and Zarabandeo for clarinet and piano.