In this paper, the possibilities of using construction and demolition (C&D) waste as a reactive medium to remediate groundwater contaminated with heavy metals (Cu, Zn) were examined. For this purpose, laboratory tests on the properties of building concrete waste, e.g., paving stones, and mixtures of waste were carried out. The scope of the laboratory test covered the physical and chemical properties of materials, as well as their removal efficiency–kinetic batch tests. During the batch tests, a pseudo-second order kinetic model was best fitted to the adsorption of selected metal ions onto the concrete waste material with high values of correlation coefficients R2. Test results indicate that concrete waste materials have a potential to be reactive medium in groundwater remediation.