A representative for the actor said Landau had been briefly hospitalized at the UCLA Medical Center in Los Angeles, California.
Dick Guttman, a publicist for Landau, told the Associated Press that the actor died of "unexpected complications", but did not provide additional details.
Born in Brooklyn, New York, in 1928, Landau began his creative career as a cartoonist for the New York Daily News at age 17, but gave up the work five years later to concentrate on theater.
Landau, left, with Johnny Depp in Ed Wood.
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More recently, Landau earned Emmy noms for playing the father of Anthony LaPaglia's character on CBS' Without a Trace and guest-starring as an out-of-touch movie producer on HBO's Entourage. "To this day, I can still hear my mother's voice saying, 'You did what?!'" He also appeared in films throughout the 1960s such as Cleopatra and The Greatest Story Ever Told before he was cast on "Mission: Impossible".
After winning the Oscar in March 1995, Landau gushed: "My God!" "But I knew if I took that job I would never leave, so I quit". Years later, he taught at the group's second location, in West Hollywood, CA, the Actors Studio West.
He said: "Everything that has happened to me is of value to me".
Infamously, Landau passed on the role of Spock in the original Star Trek.
He would go on to star in another enormously popular, franchise-spawning television series, Mission: Impossible, for three years. Or I was getting up to bat and no one was pitching to me. I thought I was insane. It would mark the first of two small-screen collaborations for the couple, who later co-starred in the 1970s science-fiction program Space: 1999. Long time member of the actor's studio and brilliant craftsman in our tradition.
He is survived by daughters Susan Landau Finch and Juliet Landau.