The Austrian actor, who won an Oscar for his role in the 1961 film Judgment at Nuremberg, died overnight at a clinic in Innsbruck after “a sudden and serious illness”, his agent said.
Maximilian Schell had been treated for pneumonia earlier this week.
He was one of the most famous German-speaking actors to have gained international fame.
The actor’s wife was reportedly at his bedside when he died.
Maximilian Schell had been in filming in Austria when he fell ill last Saturday.
He was taken to hospital and treated for a lung infection, but discharged on Tuesday.
Born in the Austrian capital, Vienna, in 1930, Maximilian Schell was one of four children of a Swiss author and an Austrian actress.
His parents emigrated to Switzerland eight years later when Austria was annexed by Nazi Germany.
A stage actor, Maximilian Schell began his Hollywood career in the late 1950s when he starred alongside Marlon Brando in the World War Two film, The Young Lions.
In 1961, Maximilian Schell was awarded an Oscar for best actor for his role as the defense lawyer of a Nazi war criminal.
The cast also included Marlene Dietrich, Burt Lancaster and Spencer Tracy.
Over the next three decades, Maxmilian Schell appeared in numerous big US productions.
His diverse characters ranged from a museum treasure thief in Topkapi (1964), to a mad scientist in sci-fi film The Black Hole (1979), to a Russian KGB colonel in Candles in the Dark (1998).
Maximilian Schell featured in a large number of international TV productions. His part as communist revolutionary Vladimir Lenin in series Stalin earned him a Golden Globe in the early 1990s.
Maximilian Schell also directed several movies, including his 1984 Oscar-nominated documentary Marlene, about Marlene Dietrich.
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