The cause of death was not announced but he had suffered from cancer for several years.
Sander, also a veteran of the Berlin stage, was best known to foreign audiences for his 1981 turn in Wolfgang Petersen's World War II epic "Das Boot" as a shell-shocked German submarine captain.
In the film, Sander famously delivers a drunken speech to his comrades mocking both the British and Adolf Hitler.
Director Volker Schloendorff cast him in his Oscar-winning adaptation of Gunter Grass' novel "The Tin Drum" as the alcoholic trumpeter Meyn.
And in 1987, he starred as the angel Cassiel in Wim Wenders' surrealist drama about Germany's painful Cold War division, "Wings of Desire", and its 1993 sequel "Faraway, So Close".
Born in 1941 in the northern city of Hanover, Sander became one of the top theatre actors in West Berlin and later the reunited capital.
His distinctive baritone was put to good use in dubbing work and narration, and in the gritty television crime show "Polizeiruf 110".
Sander was also a fixture of Berlin social life with his family of actors: wife Monika Hansen and step-children, Ben and Meret Becker.
"We have lost one of our greatest artistic personalities and an unforgettable speaking voice," Mayor Klaus Wowereit said.