Szyszlo was born in Lima, Peru; his mother was a Peruvian citizen of Mestizo ethnicity, and his father was a geographer from Poland.

After his graduation in 1948, he traveled to Europe where he studied the works of the masters, particularly Rembrandt, Titian and Tintoretto, and absorbed the varied influences of Cubism, Surrealism, Informalism, and abstraction.

While in Paris he met Octavio Paz and André Breton and was part of the group of expatriate Latin American artists and writers who met regularly at the Café de Flore, engaging in vigorous discussions on how they could participate in the international modern movement while preserving their Latin American cultural identity.

Upon his return to Peru, Szyszlo became a major force for artistic renewal in his country breaking new ground by expressing a Peruvian subject matter in a non-representational style.

Their second son, Juan Lorenzo, a dual American-Peruvian citizen, was killed in the crash of Faucett Perú Flight 251, near Arequipa on 29 February 1996, aged 36, when he was heading to the city to oversee an exhibition of his father's work there.