Zika virus (ZIKV) is an emerging arbovirus of the Flaviviridae family. Although ZIKV infection is typically mild and self-limiting in healthy adults, infection has been associated with neurological symptoms such as Guillain-Barré syndrome, and a causal link has been established between fetal microcephaly and ZIKV infection during pregnancy. These risks, and the magnitude of the ongoing ZIKV pandemic, have created an urgent need for the development of animal models to study the immune response to ZIKV infection. Previous animal models have primarily focused on pathogenesis in immunocompromised mice. In this study, we provide a model of ZIKV infection in wild-type immunocompetent C57BL/6 mice, and have provided an analysis of the immune response to infection. We evaluated the activation of several innate immune cell types, and studied the kinetics, phenotype, and functionality of T cell responses to ZIKV infection. Our results demonstrate that ZIKV infection is mild in wild-type immunocompetent C57BL/6 mice, resulting in minimal morbidity. Our data establish that at the peak of the adaptive response, antigen-experienced CD4+ T cells polarize to a Th1 phenotype, and antigen-experienced CD8+ T cells exhibit an activated effector phenotype, producing both effector cytokines and cytolytic molecules. Furthermore, we have identified a novel ZIKV CD8+ T cell epitope in the envelope protein that is recognized by the majority of responding cells. Our model provides an important reference point that will help dissect the impact of polymorphisms in the circulating ZIKV strains on the immune response and ZIKV pathogenesis. In addition, the identification of a ZIKV epitope will allow for the design of tetramers to study epitope-specific T cell responses, and will have important implications for the design and development of ZIKV vaccine strategies.