The common marmoset (Callithrix jacchus) is of considerable biomedical importance, yet there remains a need to characterize the evolutionary forces shaping empirically observed patterns of genomic variation in the species. However, two uncommon biological traits potentially prevent the use of standard population genetic approaches in this primate: a high frequency of twin-births and the prevalence of hematopoietic chimerism. Here we characterize the impact of these biological features on the inference of natural selection, and directly model twinning and chimerism when performing inference of the distribution of fitness effects to characterize general selective dynamics as well as when scanning the genome for loci shaped by the action of episodic positive and balancing selection. Results suggest a generally increased degree of purifying selection relative to human populations, consistent with the larger estimated effective population size of common marmosets. Furthermore, genomic scans based on an appropriate evolutionary baseline model reveal a small number of genes related to immunity, sensory perception, and reproduction to be strong sweep candidates. Notably, two genes in the major histocompatibility complex were found to have strong evidence of being maintained by balancing selection, in agreement with observations in other primate species. Taken together, this work, presenting the first whole-genome characterization of selective dynamics in the common marmoset, thus provides important insights into the landscape of both persistent and episodic selective forces in this species.