Doris Mary Kappelhoff was born on April 3, 1922, in Cincinnati, Ohio, the daughter of Alma Sophia (née Welz; 1895–1976) and William Joseph Kappelhoff (1892–1967). Her mother was a homemaker, and her father was a music teacher and choirmaster. Her paternal grandfather and grandmother were Dutch and German, respectively.  For most of her life, Day reportedly believed she had been born in 1924 and reported her age accordingly; it was not until her 95th birthday – when the Associated Press found her birth certificate, showing a 1922 date of birth – that she learned otherwise.
The youngest of three siblings, she had two older brothers: Richard (who died before her birth) and Paul, two to three years older. Due to her father's alleged infidelity, her parents separated. She developed an early interest in dance, and in the mid-1930s formed a dance duo with Jerry Doherty that performed locally in Cincinnati. A car accident on October 13, 1937, injured her right leg and curtailed her prospects as a professional dancer.