Actors Aaron Eckhart and Hope Davis were part of the jury who awarded the film the Best Narrative Feature prize, while Sibel Kekilli won Best Actress for her role as a mum who leaves an abusive husband by fleeing with her son from Turkey to Germany.
A statement from the judging committee says, "(When We Leave) examines one woman's struggle for personal freedom. It's a theme that is often explored - but rarely told with such humanity, subtlety, craftsmanship or immediacy."
The Best Actor title went to Eric Elmosnino, who portrayed French musician Serge Gainsbourg in Gainsbourg, Je t'Aime... Moi Non Plus, reports the Associated Press.
The New York festival, co-founded by Robert De Niro, comes to a close on Sunday (02May10).