Though her father, Vasily Geltzer, an outstanding mime dancer and regisseur of the Bolshoi Theatre, believed her physique was unsuitable for dancing, Yekaterina persuaded him to enroll her at eight in the Bolshoi's ballet school. There she developed strong pointe and pirouette technique under her teacher Joseph Mendes and graduated in 1894. After two years with the Bolshoi company, she went to St. Petersburg to study with Christian Johansson, who helped her attain the elegant grace that earned her the title “queen of adagio.” In 1901 she became prima ballerina. Though she danced in most of the classic ballets at the Bolshoi, including Swan Lake, The Sleeping Beauty, and Coppélia, she excelled in dramatic roles and in the so-called demi-caractère style of dance, in which classical ballet technique is used to perform character dance. She also performed in Paris (1910) with the Diaghilev company and in London (1911) with the famous Russian dancer and teacher Vasili Tikhomirov, whom she later married.

After the Revolution of 1917, Geltzer remained with the Moscow company, and in 1927 she created one of her most famous roles, that of Tao-Hoa, the self-sacrificing heroine of The Red Poppy who dies to save the life of a Soviet captain. Her career at the Bolshoi spanned more than 40 years, and she was one of the first to receive (1925) the title People's Artist of the Russian Soviet Federated Socialist Republic.