Characterizing how climate change will alter the burden of infectious diseases has clear public health implications. Despite our uniquely detailed understanding of the transmission process for directly transmitted immunizing infections, the impact of climate variables on these infections remains understudied. Here, we develop a novel approach that incorporates statistical analysis of climate effects with a mechanistic model of disease transmission, to investigate the dynamic response of directly transmitted, immunizing infections to climate change. We analyze the effect of climate on varicella, a common airborne childhood infection, by leveraging 30 years of reported cases across 32 states in Mexico. We use this to map the potential changes in the magnitude and variability of varicella incidence in Mexico as a result of predicted changes in future climate conditions. Our results indicate that the predicted decrease in relative humidity in Mexico towards the end of the century will increase incidence of varicella, all else equal. These changes in incidence will be non-uniform across the year such that cases will shift from winter to summer months. Climate-driven changes to the timing of future incidence, for these types of infections, may have substantial public health implications.