A model for transient infiltration into a periodically fractured porous layer is presented. The fracture is treated as a permeable-walled slot and the moisture distribution is in the form of a slug behind an advancing meniscus. The wicking of moisture from the fracture to the unsaturated porous matrix is a nonlinear diffusion process and is approximated by self-similar solutions. The resulting model is a nonlinear Volterra integral equation with a weakly singular kernel. Numerical analysis provides solutions over a wide range of the parameter space and reveals the asymptotic forms of the penetration of this slug in terms of dimensionless variables arising in the model. The numerical solutions corroborate asymptotic results given earlier by Nitao and Buscheck (1991), and by Martinez (1988). Some implications for the transport of liquid in fractured rock are discussed.