His first stage appearance was in 1948. In 1950, he was hired by the theater of Neustrelitz. In the following years, he worked in several other theaters, including the Freie Volksbühne in Berlin. He became well-known in the following decades, often playing the role of the young lover or a comic Berliner. He also dubbed Marlon Brando in German films.
Juhnke began appearing often on German television after 1977. He first played in television series with actors such as Grit Böttcher and Eddie Arent and later hosted the ZDF television show Musik ist Trumpf (Music is Trump), which was seen by up to 30 million television viewers. His role model for the show was Frank Sinatra, whose style of dress and singing he emulated. Juhnke's most popular song was a German rendition of Sinatra's signature song "I Did It My Way".
In 1992, Juhnke experienced a comeback as a film actor. He won praise from critics for character parts in the movies Schtonk!, Der Papagei (The Parrot), and Der Hauptmann von Köpenick (The Captain of Köpenick). In 1995, he played the lead role in the movie Der Trinker (The Drinker), based on the autobiography of German writer Hans Fallada. In working on this film, Juhnke drew on his own experiences with alcoholism.
His first marriage was to the actress and dancer Sybil Werden. The couple had two children: their daughter Barbara was born in 1953, and in 1956 they had a son, Peer. In 1971, Juhnke married actress Susanne Hsiao, daughter of a Chinese restauranteur and an East Prussian mother. Their son Oliver Marlon was born in 1972.
Juhnke's battle with alcohol was reported widely in the German tabloids and was followed closely by the public. In December 2001, suffering from Korsakoff's syndrome as a result of his alcohol abuse, he was hospitalized in a nursing home for patients with mental illnesses in Fredersdorf, Brandenburg.
- 1978 Goldener Vorhang (Golden Curtain) award of Berlin's "Theaterclub"
- 1980 Goldene Kamera (HÖRZU)
- 1990 Goldene Europa – Honored as an entertainer of the 80s and 90s
- 1992 Deutscher Filmpreis
- 1992 Bambi
- 1993 Ernst-Lubitsch-Preis
- 1993 Bayerischer Fernsehpreis
- 1993 Karl-Valentin-Orden
- 1993 Romy – Most popular television actor of the year
- 1995 Critic's Award of the Berliner Zeitung for lifetime accomplishment
- 1996 Telestar
- 1998 Goldener Löwe (RTL)
- 2000 Goldene Kamera (HÖRZU)