Indigenous Australians experience poorer oral health than non-Indigenous Australians despite closing-the-gap initiatives. Cultural competence is an important skill in the delivery of oral health care. The need for academic institutions to incorporate Indigenous culture more widely into their curricula to improve educational outcomes for Indigenous peoples and to increase cultural competence for all students has been recognized. The aims of this study were to identify students’ perceptions of Indigenous content in current dental and oral health curricula; perceived barriers and supports for developing students’ Indigenous cultural competence; and recommended strategies to inform future education in Indigenous culture. Students in the Doctor of Dental Medicine (DMD) and Bachelor of Oral Health (BOH) programs at the University of Sydney participated in semi-structured interviews to explore barriers and supports to students’ becoming more competent in Indigenous culture. Thematic analysis was used to synthesize the students’ responses. Fifteen students participated in interviews. In analysis of the data, five key themes emerged: defining Indigenous cultural competence; current Indigenous cultural content; barriers to incorporating Indigenous education; future Indigenous curricular content and strategies; and diversity within student cohorts. These findings suggest that increasing Indigenous cultural competence among dental and oral health students requires an informed history of Indigenous Australians, engagement with Indigenous communities, and reflection on these experiences. Additionally, recruitment of Indigenous staff and students in the school will facilitate culturally appropriate ways to redress Indigenous health disparities and increase the overall health of Indigenous peoples.