A Japanese American, Tajiri was born in Watts, a working-class neighborhood of Los Angeles.
He was the fifth of seven children born to Ryukichi Tajiri and Fuyo Kikuta, first generation emigrants (issei), who moved from Japan to the United States in 1906 and 1913.
In 1942, following the signing of Executive Order 9066, Tajiri's family was incarcerated at Poston War Relocation Center in Arizona.
He met Karel Appel and Corneille in Paris and shows at the 1949 COBRA exhibition at the Stedelijk Museum, Amsterdam.
From 1969 Tajiri Shinkichi taught at the Hochschule für Bildende Künste at Berlin.