Miller died on Thursday night at his home in Roxbury, Connecticut, of heart failure with his family at his bedside his assistant, Julia Bolus, said on Friday.
His plays, with their strong emphasis on family, morality and personal responsibility, spoke to the growing fragmentation of American society.
"A lot of my work goes to the centre of where we belong - if there is any root to life - because nowadays the family is broken up, and people don't live in the same place for very long," Miller said in a 1988 interview.
"Dislocation, maybe, is part of our uneasiness. It implants the feeling that nothing is really permanent."
Miller's career was marked by early success. He was awarded the Pulitzer Prize for Death of a Salesman in 1949, when he was just 33 years old.
His marriage to screen star Marilyn Monroe in 1956 further catapulted the playwright to fame, though that was publicity he said he never pursued.
"Dislocation, maybe, is part of our uneasiness. It implants the feeling that nothing is really permanent"
Arthur Miller, playwright
In a 1992 interview with a French newspaper, he called her "highly self-destructive" and said that during their marriage, "all my energy and attention were devoted to trying to help her solve her problems. Unfortunately, I didn't have much success."
Death of a Salesman, which took Miller only six weeks to write, earned rave reviews when it opened on Broadway in February 1949, directed by Elia Kazan.
The story of Willy Loman, a man destroyed by his own stubborn belief in the glory of American capitalism and the redemptive power of success, was made into a movie and staged all over the world.
"I couldn't have predicted that a work like Death of a Salesman would take on the proportions it has," Miller said in 1988.
Miller married Marilyn Monroe (L)
"Originally, it was a literal play about a literal salesman, but it has become a bit of a myth, not only here but in many other parts of the world."
In 1999, 50 years after it won the Tony Award as best play, Death of a Salesman won the Tony for best revival of the Broadway season. The show also won the top acting prize for Brian Dennehy, who played Loman.
Miller, then 83, received a lifetime achievement award.
"Just being around to receive it is a pleasure," he joked to the audience during the awards ceremony.
Miller won the New York Drama Critics' Circle's best play award twice in the 1940s, for All My Sons in 1947 and for Death of a Salesman.
In 1953, he received a Tony Award for The Crucible, a play about mass hysteria during the Salem witch trials that was inspired by the repressive political environment of McCarthyism.
That play, still read by thousands of American high-school students each year, is Miller's most frequently performed work.