Moisture damage in asphalt mixtures is defined as the gradual loss of structural integrity caused by the presence of moisture. A simple experimental procedure was developed in this study to measure water vapor diffusion coefficients in coarse aggregates, fine aggregate mixture (blend of the fine portion of the aggregates with the asphalt binder), and hot-mix asphalt. The procedure is based on periodic weight measurements of specimen-container ensembles subjected to a controlled temperature and relative humidity environment. Fick's first law was used to estimate the diffusion coefficients of the materials. The results show that the proposed experimental method is an economic and efficient tool to quantify water vapor diffusion coefficients. Determining these material properties is fundamental to develop numerical models to study the deleterious effects of moisture vapor on the mechanical performance of asphalt mixtures. In order to exemplify the significance of the experimental measurements, a numerical simulation of transient moisture diffusion within the cross section microstructure of an asphalt mixture was conducted. The results of the simulations suggest that diffusion coefficients are fundamental for tracking the potential of a mixture to develop moisture-related degradation processes. Furthermore, it was observed that under the same environmental conditions, moisture damage in an asphalt mixture is highly influenced by the moisture diffusion coefficient of its constitutive phases.