Schell died following "a sudden and serious illness," agent Patricia Baumbauer said.
The actor took ill on January 18 in Kitzbuhel, western Austria, where he was filming for German channel ZDF, the Austrian news agency APA reported.
He died after leaving the hospital on Tuesday, APA reported after having initially said he died overnight in a clinic in the western Austrian city of Innsbruck.
Born in Vienna, before fleeing with his parents into exile in Switzerland following Austria's annexation by the Nazis in 1938, he returned to Austria after the war and later became a successful Hollywood actor.
In 1961, he won an Oscar for best actor for his role as a lawyer for a Nazi war criminal in Stanley Kramer's "Judgment at Nuremberg." He starred with Marlene Dietrich, Burt Lancaster, Spencer Tracy and Richard Widmark.
Spending a long time in the shadow of his older sister Maria Schell, who had also broken into Hollywood, Maximilian Schell started at the age of 23 as a stage actor in the Swiss town of Basel.
He remained faithful to the theatre until his later years, acting in 2000 in a stage version of "Judgment at Nuremberg," and in London in 2006 he acted in a Robert Altman production of an Arthur Miller play, "Resurrection Blues".
In cinema, he made his Hollywood debut in 1958 at 28 years old, acting beside Marlon Brando in "The Young Lions," a film by Edward Dmytryk.