Mueller was born in Hamburg, Germany, in 1924 and immigrated to America at the age of 15. Her father, Fritz C. Neumann, was a professor at Evansville College. Her mother died in 1953. "Though my family landed in the Midwest, we lived in urban or suburban environments," she once wrote. She and her husband, Paul Mueller (d. 2001) built a home in Lake Forest, Illinois in the 1960s, where they raised two daughters and lived for many years. Mueller currently resides in a retirement community in Chicago. Her poems are extremely accessible, yet intricate and layered. While at times whimsical and possessing a sly humor, there is an underlying sadness in much of her work.