Day was born Doris Mary Anne Kappelhoff on April 3, 1922, in Cincinnati, Ohio, the daughter of German-American parents Alma Sophia (née Welz; 1895–1976) and William Joseph Kappelhoff (1892–1967). She was named after actress Doris Kenyon. Her mother was a homemaker, and her father was a music teacher and choirmaster. Her paternal grandfather Franz Joseph Wilhelm Kappelhoff immigrated to the United States in 1875 and settled within the large German community in Cincinnati. For most of her life, Day stated that she was born in 1924, but on the occasion of her 95th birthday, the Associated Press found her birth certificate that showed a 1922 year of birth.
Day had two older brothers: Richard (1917–1919), who died before her birth, and Paul (1919–1957). Her father's infidelity caused her parents to separate in 1932 when she was 10. She developed an early interest in dance, and in the mid-1930s formed a dance duo with Jerry Doherty that performed in nationwide competitions. She had signed a contract with a casting company to be a dancer and she was preparing to move to Los Angeles to pursue this opportunity. Family friends that lived just north of Cincinnati, in Hamilton, Ohio planned a going away party for her but tragedy struck on her way to the party. On October 13, 1937, while Day was riding with friends, their car collided with a freight train, and she broke her right leg, curtailing her prospects as a professional dancer.
