New York City Mayor Fiorello H. LaGuardia started the high school in 1936, an event he described as "the most hopeful accomplishment" of his administration. As the mayor of New York City he wanted to establish a public school in which students could hone their talents in music, art and the performing arts. Music & Art was made up of three departments: Art, Instrumental Music, and Vocal Music. It was a magnet school, meant to draw talented students from all boroughs. In 1948, a sister school–the High School of Performing Arts–was created in an effort to harness students' talents in dance.
Future Mad magazine contributors Al Jaffee, Will Elder, Harvey Kurtzman, John Severin, and Al Feldstein all attended Music & Art together in the 1930s. Comic book artists Ross Andru and Mike Esposito, did as well, although they were slightly younger than Jaffee and the others.
R. O. Blechman, Milton Glaser, Ed Sorel, and Reynold Ruffins–three of the four co-founders of the design firm Push Pin Studios–were M&A students in the 1940s. Other M&A graduates from the 1940s include Bess Myerson, Allan Kaprow, and Hal Linden. Notable graduates from the 1950s include Gloria Davy, Diahann Carroll, Susan Stamberg, Jonathan Tunick, , Peter Yarrow, Tony Roberts, James Burrows, Erica Jong, Felix Pappalardi, and Jeremy J. Shapiro.