The book is based on a short story by Palmer's husband Theodor Geisel (Dr. Seuss), "Gustav, the Goldfish", which was published with his own illustrations in Redbook magazine in June 1950.

When the boy inadvertently disobeys these instructions out of compassion for his new pet, Otto begins to grow uncontrollably, quickly outgrowing his fishbowl.

This leads the boy to move him into a series of successively larger containers, ending with the bathtub.

"[6] Palmer's work involved, in part, rewriting and simplifying the original text to comply with Beginner Books' policies.

She finished A Fish Out of Water in 1961, at the Hotel Madison in New York City where she and her husband were staying for six weeks while their home in La Jolla, California, was being remodeled.