Klemperer was born in Cologne, Germany, to a musical family, but he said that he had little musical aptitude. His father was renowned conductor Otto Klemperer and his mother was soprano Johanna Geisler. He had a younger sister named Lotte (1923–2003). His father was Jewish by birth; he converted to Catholicism, but later returned to Judaism. His mother was Lutheran. Otto Klemperer was a first cousin of Victor Klemperer.
The Klemperer family emigrated to the United States in 1935, settling in Los Angeles, where Otto Klemperer became conductor of the Los Angeles Philharmonic. Werner Klemperer began acting in high school and enrolled in acting courses at the Pasadena Playhouse before joining the United States Army to serve in World War II. While stationed in Hawaii, he joined the Army’s Special Services unit, spending the next years touring the Pacific entertaining the troops. At the war’s end, he performed on Broadway before moving into television acting.
He broadened his acting career by performing as an operatic baritone and a singer in Broadway musicals. He can also be heard as the Speaker in Arnold Schoenberg’s Gurre-Lieder, in a 1979 live performance with the Boston Symphony Orchestra.