"The Reluctant Fundamentalist" was chosen to "highlight the growing role of female creativity in all spheres of culture and contemporary society", Alberto Barbera, the director of this year's festival, was quoted as saying by Xinhua.
Female influence is an important theme of the festival, during which people will see multiple activities to promote awareness on female contribution to world cinema.
At a press conference before the opening of the event, Nair said: "I made the movie to promote dialogue between West and East, and I hope it will help to break the wall between different cultures, races and religions."
"For myself, I felt equal intimacy to both cultures," said the Indian director who has lived in New York for many years.
The movie, adapted from a book with the same tile, would "provide much food for thought", said Barbera.
The Lido island, where the event is staged, is now abuzz with well-known directors, actors and actress.
However, big names like George Clooney, Angelina Jolie and Johnny Depp did not appear in the red carpet show in the evening as in past years.
This year's festival will feature 18 movies in the competition rounds, with dozens more appearing in out-of-competition and Horizon sessions.