Bergman won three Oscars for Best Foreign Language Film, for The Virgin Spring, Through a Glass Darkly and Fanny and Alexander. He also won the Irving G. Thalberg Memorial Award, presented at the 1971 Oscars ceremony.
Eva Bergman said that her father had passed away "peacefully."
For many movie buffs, Bergman was the greatest of the authorial film-makers of the 1950s and 1960s, outranking even such figures as Federico Fellini, Luis Bunuel or Jean-Luc Godard.
The demanding nature of his work, in particular the gravity of his themes, was such that the general public found him remote, and he was accused in his homeland of being partly responsible for Sweden being presented as a country of neurotics.
Born in 1918 in Uppsala to a Lutheran minister, Bergman became interested in theatre and cinema after leaving Stockholm University, where he never completed his course in literature and art.
Bergman started making films soon after the Second World War. An early film to catch international attention was Summer with Monika (Sommaren med Monika). The nude scenes in the film were controversial abroad, and were credited by some with giving Sweden its reputation as a sexually liberated country.
A number of Swedish actors worked repeatedly with Bergman, including Max von Sydow, Bibi Andersson, Harriet Andersson, Erland Josephson, Gunnar Björnstrand and Liv Ullmann.
Commenting on his death on Monday, Bibi Andersson told tabloid Aftonbladet that she would "miss him enormously."
Known in Sweden mainly as a dramatist, Bergman obtained poor reviews for work that was considered dark and incomprehensible, with its focus on love, loneliness, anguish and relations with God.
Women also occupied a central role in his work, which often dwelt on the mysteries of the female soul. He had loved his mother intensely as a child, and when a doctor advised her to set him aside or he would be damaged for life, he felt the loss deeply.
Mother-son relationships featured prominently in his work, as did his experiences from five marriages.
Bergman made profoundly personal films following his intellectual and spiritual preoccupations and tracing his loss of faith in God.
Bergman's films tended to be low-budget, with Cries and Whispers (1973) costing only $200,000. Aside from the Oscar winners, Bergman received widespread critical acclaim for films including The Seventh Seal (Det Sjunde Inseglet - 1957) Wild Strawberries (Smultronstället -1957) and his 1973 television series Scenes from a Marriage (Scener ur ett Äktenskap).
Fanny and Alexander (1984) was his last major feature, and is regarded as one of his best. He kept working well into old age, producing his last television series, Saraband, in 2003.
Bergman was also an accomplished stage director, and managed and directed both the Malmö City Theatre and the Stockholm Royal Dramatic Theatre (Dramaten). He was also director of the Residenz-Theater of Munich between 1977-84, a period that coincided with a dispute with the Swedish authorities over alleged tax evasion.
Four of Bergman's marriages ended in divorce. His last wife, Ingrid, died in 1995. He had nine children, including one, daughter Linn Ullmann, from his relationship with actress Liv Ullman.