The cleaning of porous materials is a ubiquitous and complex problem. Owing to the structure of such materials, surface contamination may ingress inside the pore space and become poorly accessible to a surface washing flow. Contaminant redistribution−where the washing flow encourages the contaminant to spread over the porous surface, resulting in additional contaminant absorption downstream−makes it very difficult to monitor the levels of contamination throughout the material and determine whether cleaning has been successful. To obtain a quantitative understanding of contaminant redistribution in porous media, we propose a two-dimensional model for the surface washing of a wet porous medium contaminated by a drop of a single-species contaminant. We consider porous media of negligible permeability but finite porosity. A coupled mass transport problem describes the concentration of contaminant in the surface washing flow and in the porous medium. Advection and diffusion processes are considered in the surface washing flow while, in the negligible permeability limit, mass transport in the porous medium is governed by molecular diffusion. We focus our analysis on asymptotic regimes that exhibit contaminant redistribution in the porous medium and substantiate our results through a comparison with numerical simulations performed in COMSOL. The results of this investigation are used to suggest ways in which the cleaning process in porous materials can be improved to reduce the impact of contaminant redistribution and, ultimately, the levels of residual contamination left behind after cleaning has taken place.