Scientific interest in genomics in Africa is on the rise with a number of funding initiatives aimed specifically at supporting research in this area. Genomics research on material of African origin raises a number of important ethical issues. A prominent concern relates to sample export, which is increasingly seen by researchers and ethics committees across the continent as being problematic. The concept of genomic sovereignty proposes that unique patterns of genomic variation can be found in human populations, and that these are commercially, scientifically or symbolically valuable and in need of protection against exploitation. Although it is appealing as a response to increasing concerns regarding sample export, there are a number of important conceptual problems relating to the term. It is not clear, for instance, whether it is appropriate that ownership over human genomic samples should rest with national governments. Furthermore, ethnic groups in Africa are frequently spread across multiple nation states, and protection offered in one state may not prevent researchers from accessing the same group elsewhere. Lastly, scientific evidence suggests that the assumption that genomic data is unique for population groups is false. Although the frequency with which particular variants are found can differ between groups, such genes or variants per se are not unique to any population group. In this paper, the authors describe these concerns in detail and argue that the concept of genomic sovereignty alone may not be adequate to protect the genetic resources of people of African descent.