The 41-year-old actress has joined Cate Blanchett, Kristen Wiig and Billy Crudup in the movie, written by Linklater, Holly Gent Palmo and Vince Palmo, reported Deadline.
The film, based on Maria Semple's novel, follows Bernadette Fox (Blanchett), an architect-turned-recluse who goes missing prior to a family vacation.
Greer will play Dr Kurtz, the brutally honest director of a treatment facility that caters to mental illness and drug issues.
Megan Ellison of Annapurna Pictures is producing along with Color Force Productions' Nina Jacobson and Brad Simpson.