Allen Say was born in Yokohama, Japan, to a Japanese family: a Japanese American mother and a Korean father who was adopted by British parents. At age 12, four years after his parents' divorce, Say went to live with his grandmother, but received her permission a short time later to live alone. The boy apprenticed himself for many years to his favorite cartoonist, Noro Shinpei, an experience detailed in his autobiographical novel The Ink-Keeper's Apprentice. In time Say came to think of Shinpei as his "spiritual father," as well as a mentor.

When his father decided to move to the United States with his new family, Allan Say was invited to come along. He attended military school for a short time, an experience that was decidedly negative: "I learned bad English from rich juvenile delinquents and developed a lifelong loathing for uniforms and professional soldiers." He was eventually expelled for smoking a cigarette. In the years before becoming a full-time author and illustrator, Say worked as a sign painter and photographer, as well as being drafted into the U.S. Army for a time. While stationed in Germany, his photography was noted and eventually published in the magazine, Stars and Stripes. Upon returning to the United States, he pursued photography as a career choice, but was encouraged to explore his illustrations. He was approached by Houghton Mifflin with a retelling of the Japanese folktake, "The Boy of the Three-Year Nap."

In 1994, fellow children's author Lois Lowry mentioned Say in her Newbery Award acceptance speech for The Giver, having discovered the day of the ceremony that in childhood, both authors lived in the same Japanese town, Shibuya. The two authors spoke for the first time when each autographed a book for the other and she signed hers in Japanese.

Say currently lives in Portland, Oregon.