This article looks at Melbourne’s Islamic Museum of Australia. It examines how the museum tells a story of an “Australian Islam” through its use of material and artistic objects; how it symbolises and synthesises the assumed binary of east and west, through spatial expressions that narrate a religious community’s “growing up” in a changing urban and Australian context. Furthermore, it looks at how the curators, intentionally or otherwise, deal politically with the Muslim community’s affective relationships that are shaped by their experiences as a minority that endures a persistent Islamophobia. And, thus, most importantly, this article concludes by examining the role the museum’s material artefacts play in intercultural relations within a multicultural Australia. Using Nietzsche’s The Birth of Tragedy, I argue the museum reflects an Apollonian sense of art that relegates, and attempts to control, the wilder excesses of a Dionysian and communal spirit. The Apollonian view translates to an expressive and abstract celebration of liberal myths about progress and individuality that purposely relegates the more dangerous struggles of Muslim immigrants dealing with the conditions of a Dionysian postcolony. The museum rather than tell a balanced story of Australian Muslims ends up telling a story about the ideological limits of what multiculturalism allows us to say about being Muslim and Australian.