Following the 2023 publication of the International Olympic Committee's criteria for the reinstatement of Russian athletes (they were suspended in February 2022 due to the Russian invasion of Ukraine), athletes affiliated with CSKA Moscow were officially prohibited from attending the Olympic Games until at least 2026.

Elena Mukhina, the 1978 World Champion artistic gymnast, Aliya Mustafina and Yevgeniya Kanayeva, Olympic gold medalists in gymnastics, Sofya Velikaya, a sabre fencer, Olympic champions Elena Vesnina, and Viktor An.

The club was created as the "Experimentally demonstrative Military Sports field of Vsevobuch" (OPPV) in February 1923 by the Central Administration of Military Training for workers based on the pre-revolutionary "Society of Ski Sports Amateurs" (OLLS).

In February 1928 the club was included to the newly established the Frunze Central House of Red Army (CDKA) as a department of physical culture and sports.

In October 1953 all sports centers of CDKA and Air Force of the Moscow Military District were included in the Central Sports Club of Ministry of Defense (CSK MO), which in April 1960 it was renamed into its more common title - the Central Sports Club of the Armed Forces (CSKA), which the Moscow branch belonged as the flagship and most elite of all the clubs within the Soviet Armed Forces.