Kate Winslet and Josh Brolin had previously landed roles in the adaptation of the Joyce Maynard novel of the same name.
The coming-of-age drama follows Henry, a man in his thirties who recounts an eventful Labour Day weekend when he was 13 years old.
Suits actor Tom Lipinski is also in talks to appear in the project as a younger version of Brolin's character, reports Variety.
Professional kiteboarder Monroe will play Mandy, a girl he meets in Vietnam who later becomes his wife and mother of his child.
Monroe will next star as Zac Efron's love interest in an as-yet untitled project from Ramin Bahrani.
The actress is currently filming Sofia Coppola's The Bling Ring alongside Emma Watson and Kirsten Dunst.