Salinger passed away peacefully at his home in New Hampshire on Wednesday, Phyllis Westberg, his agent at Harold Ober Associates in New York, said.
Published in 1951, "Catcher in the Rye" and its anti-hero protagonist Holden Caulfield quickly become cultural touchstones at a time of immense demographic and social change in the US.
One of the first books to accurately reflect the alienation felt by many teenagers, it detailed the experiences of Caulfield, 17, after he was expelled from an elite school.
Salinger, in one of his rare interviews, revealed that the main character was based on his own experiences as a youth. The book was Salinger's only published novel, though several volumes of short stories and novellas were also successful.
Born in New York in 1919, he served in World War II in the US military and was one of the first soldiers to enter a liberated concentration camp. Salinger published several stories during the 1940's in magazines such as Collier's, but got his big break when The New Yorker accepted his short story, "A Perfect Day for Bananafish", in 1948.
Salinger largely withdrew from the public eye with the controversy that surrounded "Catcher in the Rye", and never published another novel even though he is said to have written at least two others. He refused to allow any of his work to be made into films after an unsatisfactory adaptation of his book, "Uncle Wiggily in Connecticut", in 1949.
Salinger's agent said he had broken his hip in May but had recovered well until his health took a sudden turn for the worse at the beginning of this year.
"Salinger had remarked that he was in this world but not of it. His body is gone but the family hopes that he is still with those he loves, whether they are religious or historical figures, personal friends or fictional characters," Westberg said in a statement.
Salinger is survived by his wife Colleen, son Matt and daughter Margaret, and three grandsons as well as his ex-wife and mother of their children, Claire Douglas.
"In keeping with his life long, uncompromising desire to protect and defend his privacy there will be no service, and the family asks that peoples respect for him, his work, and his privacy be extended to them, individually and collectively, during this time," Westberg said.
"He will be missed by the few he was close to every bit as much as by the readers who loved reading him," Westberg said.