A small circle of family and friends, including actresses Bibi Andersson and Liv Ullman, attended the ceremony at Fårö Church, Dagens Nyheter reported.
Bergman died at his home on the island on July 30th aged 89.
Details of the funeral were not officially disclosed, and police and security guards kept media and curious onlookers at bay.
Dozens of red roses and white lilies were delivered to the church just prior to the ceremony, which began at noon, according to DN.
The Swedish flag was flying at half-mast outside the church, a white building with medieval origins.
The tabloid Aftonbladet reported that some 50 people had been invited to bid a final farewell to the cinema giant.
Bergman was buried in a simple wooden coffin made by a Swedish carpenter who helped design parts of Bergman’s beloved home on Fårö, a small island in the Baltic Ocean where the director lived as a virtual recluse.
In order to keep the date of the funeral a secret as long as possible, his grave was dug in the Fårö Church cemetery at dusk on Friday, Aftonbladet said.
Bergman will be laid to rest next to his fifth and final wife Ingrid von Rosen, who died in 1995. A shared tombstone bearing both von Rosen’s and Bergman’s names was erected after her death.
Bergman’s films won three best foreign language film Oscars. Despite his preoccupation with dark themes such as death and sexual anguish, he was widely acclaimed for perennial arthouse favourites such as “The Seventh Seal” (1957) and “Fanny and Alexander” (1982).
For many movie buffs, Bergman was the greatest of the authorial filmmakers of the 1950s and 1960s, outranking such figures as Federico Fellini, Luis Bunuel or Jean-Luc Godard.
Bergman was married five times and had nine children.
His strict childhood – his father Erik was a clergyman in Stockholm – and family relationships influenced him profoundly and were reflected in all his work.
He directed his first film “Crisis” in 1945 but it was not until 1956 that he won international acclaim when “Smiles of a Summer Night” was shown at the Cannes Festival.
For more than three decades he produced an average of a movie a year, including “Wild Strawberries” (1957), “The Virgin Spring” (1960), “Through a Glass Darkly” (1961), “Winter Light” (1963), “Scenes from a Marriage” (1973), “Autumn Sonata” (1978) and “Saraband” (2003).