Expanded carrier screening (ECS) for recessive monogenic diseases requires prior knowledge of genomic variation, including DNA variants that cause disease. The composition of pathogenic variants differs greatly among human populations, but historically, research about monogenic diseases has focused mainly on people with European ancestry. By comparison, less is known about pathogenic DNA variants in people from other parts of the world. Consequently, inclusion of currently underrepresented Indigenous and other minority population groups in genomic research is essential to enable equitable outcomes in ECS and other areas of genomic medicine. Here, we discuss this issue in relation to the implementation of ECS in Australia, which is currently being evaluated as part of the national Government's Genomics Health Futures Mission. We argue that significant effort is required to build an evidence base and genomic reference data so that ECS can bring significant clinical benefit for many Aboriginal and/or Torres Strait Islander Australians. These efforts are essential steps to achieving the Australian Government's objectives and its commitment "to leveraging the benefits of genomics in the health system for all Australians." They require culturally safe, community-led research and community involvement embedded within national health and medical genomics programs to ensure that new knowledge is integrated into medicine and health services in ways that address the specific and articulated cultural and health needs of Indigenous people. Until this occurs, people who do not have European ancestry are at risk of being, in relative terms, further disadvantaged.