Climate change impacts on infectious diseases are poorly quantified. Using data from 21 countries, we find that dengue incidence increases nonlinearly with temperature, with the largest impacts of warming at cooler temperatures, peak incidence around 28°C, and declines at higher temperatures. We estimate that 18% of dengue incidence on average in the study countries is due to historical climate change, and further project that future warming will lead to 49% to 76% increases depending on the emissions scenario, holding non-climatic factors constant, highlighting the importance of climate mitigation and adaptation. The largest increases are projected to occur in cooler areas, with potential minor decreases in warmer locations.