Katia Mann was the youngest child and only daughter of the German Jewish mathematician and artist Alfred Pringsheim and his wife Hedwig Pringsheim, who was an actress in Berlin before her marriage. Katia was also a granddaughter of the writer and women's rights activist Hedwig Dohm. Her twin brother Klaus was a conductor, composer, music writer and music pedagogue, active in Germany and Japan. She married the writer Thomas Mann.

Alfred Pringsheim was a German mathematician and patron of the arts.