It won a total of four Oscars, including best director and original screenplay for Bong Jun-ho and best international feature film.
The film is a tale of two South Korean families - the wealthy Parks and the poor Kims - that mirrors the deepening disparities in Asia's fourth-largest economy and has struck a chord with global audiences.
Koreans have been celebrating for the past week.
Local cinemas and TV channels began a rerun of the film, as well as showing Bong's other films including "Snowpiercer" and "Memories of Murder."
Bong and the cast of "Parasite" are scheduled to hold a press conference on Wednesday. (Writing by Cynthia Kim Editing by Frances Kerry)