Creating statistical models that generate accurate predictions of infectious disease incidence is a challenging problem whose solution could benefit public health decision makers. We develop a new approach to this problem using kernel conditional density estimation (KCDE) and copulas. We obtain predictive distributions for incidence in individual weeks using KCDE and tie those distributions together into joint distributions using copulas. This strategy enables us to create predictions for the timing of and incidence in the peak week of the season. Our implementation of KCDE incorporates 2 novel kernel components: a periodic component that captures seasonality in disease incidence and a component that allows for a full parameterization of the bandwidth matrix with discrete variables. We demonstrate via simulation that a fully parameterized bandwidth matrix can be beneficial for estimating conditional densities. We apply the method to predicting dengue fever and influenza and compare to a seasonal autoregressive integrated moving average model and HHH4, a previously published extension to the generalized linear model framework developed for infectious disease incidence. The KCDE outperforms the baseline methods for predictions of dengue incidence in individual weeks. The KCDE also offers more consistent performance than the baseline models for predictions of incidence in the peak week and is comparable to the baseline models on the other prediction targets. Using the periodic kernel function led to better predictions of incidence. Our approach and extensions of it could yield improved predictions for public health decision makers, particularly in diseases with heterogeneous seasonal dynamics such as dengue fever.