Given the limited effectiveness of strategies based solely on vector control to reduce dengue virus transmission, it is expected that an effective vaccine could play a pivotal role in reducing the global disease burden of dengue. Dengvaxia® from Sanofi Pasteur recently became the first dengue vaccine to become licensed in select countries and to achieve WHO recommendation for use in certain settings, despite the fact that a number of uncertainties about the vaccine's efficacy and mode of action complicate projections of its potential impact on public health. We used a new stochastic individual-based model for dengue transmission to perform simulations of the impact of Dengvaxia® in light of two key uncertainties: statistical uncertainty about the numerical value of the vaccine's efficacy against disease, and biological uncertainty about the extent to which its efficacy against disease derives from the amelioration of symptoms, blocking of dengue infection, or some combination thereof. Our results suggest that projections of the vaccine's public health impact may be far more sensitive to biological details of how the vaccine protects against disease than to statistical details of the extent to which it protects against disease. Under the full range of biological uncertainty that we considered, there was nearly three-fold variation in the population-wide number of disease episodes averted. These differences owe to variation in indirect effects of vaccination arising from uncertainty about the extent of onward transmission of dengue from vaccine recipients. These results demonstrate important limitations associated with the use of symptomatic disease as the primary endpoint of dengue vaccine trials and highlight the importance of considering multiple forms of uncertainty in projections of a vaccine's impact on public health.