Stoutenburg was born in Darfur, Minnesota. Following her father's death in 1918, she was raised by her paternal grandmother in Hanley Falls, Minnesota. She finished high school in Minneapolis, and attended the Minneapolis School of Art from 1936 to 1938. She then worked as a librarian and in other capacities near Richfield, Minnesota. In 1943, she published her first book of children's fiction, The Model Airplane Mystery. Stoutenburg later wrote, "After publishing in many magazines, I seriously settled down to writing books in 1951. She had published four books of children's fiction by 1956, when she moved to California to become an editor at Parnassus Press, a publisher of children's literature. She held the position at Parnassus Press until 1958. Over her career, Stoutenburg published about forty books of juvenile fiction and non-fiction. Several of the works were co-authored with Laura Nelson Baker, with whom Stoutenburg lived. Stoutenburg also published under the pseudonyms Barbie Arden, Lace Kendall, and Nelson Minier. At least five of Stoutenburg's books were Junior Literary Guild selections. Only one of her works, American Tall Tales, is currently in print; upon its publication in 1966, the New York Times included it on a listing of recommended volumes for children, summarizing it as "Eight tales, tough, sentimental, and bold, about American's folk heroes ...".
Stoutenburg's first volume of poetry, Heroes, Advise Us, was the 1964 Lamont Poetry Selection of the Academy of American Poets. Her second collection, A Short History of the Fur Trade, won a California Book Award (silver) for 1969, and was a close competitor for the Pulitzer Prize. Her third collection, Greenwich Mean Time, was published in 1979. James Dickey has written of her poetry, "If I were to characterize the tone of voice, I would call it that of sensitive outrage, quivering, powerful, and delicate. Delicate: therefore powerful..."
Stoutenburg died of cancer in 1982 in Santa Barbara, California. At Stoutenburg's request, David R. Slavitt subsequently edited and published a selection of her poetry. The volume, Land of Superior Mirages, includes a number of poems that had been unpublished at her death. In his review, Robert von Hallberg wrote, "Adrien Stoutenburg's poems deserve much more attention than they have received." Some of Stoutenburg's papers, and also those of Laura Nelson Baker, are archived at the University of Minnesota Children's Literature Research Collection. Papers relating to Stoutenburg's career as a poet are housed at The Bancroft Library at the University of California, Berkeley.
Stoutenburg's poems were selected for nine volumes of the annual Borestone Mountain Poetry Awards, and have been included in several more recent anthologies. One common selection is her poem "Cicada", originally published in 1957 in The New Yorker.