Covarrubias received little formal artistic training. In 1923 he went to New York City on a government scholarship, and his incisive caricatures soon began to appear in magazines such as Vanity Fair and The New Yorker. A collection of his caricatures, The Prince of Wales and Other Famous Americans, was published in 1925. His illustrations showing his interest in the study of racial types also appeared in numerous magazines and books. In 1930 and 1933 he and his wife traveled in Asia, and subsequently he wrote Island of Bali (1937). Covarrubias also painted six mural maps illustrating the cultures of the Pacific area for the Golden Gate International Exposition in San Francisco; these maps were then published as Pageant of the Pacific (1939).
After returning to Mexico in the early 1940s, Covarrubias wrote and illustrated an account of the Tehuantepec region, Mexico South (1946). His book The Eagle, the Jaguar, and the Serpent (1954) surveyed the cultures of the North American Indians. He also worked as a theatre designer, easel painter, printmaker, and art-history teacher.