Karetnikov studied at the Central Musical School (1942–1948) and the Moscow Conservatory (1948–1953) where his teachers were Vissarion Shebalin (composition), Tatiana Nikolayeva (piano), Igor Sposobin and Viktor Tsukkerman (theory).
His ballets Vanina Vannini and The Geologists were performed at the Bolshoi Theatre with choreography by Natalia Kasatkina and Vladimir Vasiliev.
His third ballet Little Zaches Called Zinnober was performed at the Hanover Opera House (1971) in the composer's absence, because he was not given permission to travel abroad.
His main activity at that time was writing incidental music for theatre, film and television.
He wrote two large scale operas Till Eulenspiegel (1965–1985) and The Mystery of Apostle Paul, (1970–1987).