Born in San Juan de los Lagos, Mexico, Izquierdo moved to Mexico City in the 1920s, where she enrolled at the Escuela Nacional de Bellas Artes. She quickly established herself within the vibrant post-revolutionary art scene, gaining recognition for her distinct technical approach and thematic commitment to Mexican heritage.

Her work is characterized by a rich, emotive use of color and a focus on subjects such as altars, circus performers, and traditional Mexican landscapes. She often employed a surrealist sensibility to explore themes of memory and national identity, distinguishing her style from the more overtly political muralism prevalent among her contemporaries.

Izquierdo remains a central figure in 20th-century Mexican art history. Her legacy continues to be examined in the context of global modernism, with her contributions frequently cited alongside other prominent Mexican artists of the era.