Prophylactic vaccination is a powerful tool for reducing the burden of infectious diseases, due to a combination of direct protection of vaccinees and indirect protection of others via herd immunity. Computational models play an important role in devising strategies for vaccination by making projections of its impacts on public health. Such projections are subject to uncertainty about numerous factors, however. For example, many vaccine efficacy trials focus on measuring protection against disease rather than protection against infection, leaving the extent of breakthrough infections (i.e., disease ameliorated but infection unimpeded) among vaccinees unknown. Our goal in this study was to quantify the extent to which uncertainty about breakthrough infections results in uncertainty about vaccination impact, with a focus on vaccines for dengue. To realistically account for the many forms of heterogeneity in dengue virus (DENV) transmission, which could have implications for the dynamics of indirect protection, we used a stochastic, agent-based model for DENV transmission informed by more than a decade of empirical studies in the city of Iquitos, Peru. Following 20 years of routine vaccination of nine-year-old children at 80% coverage, projections of the proportion of disease episodes averted varied by a factor of 1.76 (95% CI: 1.54-2.06) across the range of uncertainty about breakthrough infections. This was equivalent to the range of vaccination impact projected across a range of uncertainty about vaccine efficacy of 0.268 (95% CI: 0.210-0.329). Until uncertainty about breakthrough infections can be addressed empirically, our results demonstrate the importance of accounting for it in models of vaccination impact.