The aim of this work was to check the possibility of using a concrete matrix to immobilize contaminants from ash (fly and bottom) originating from the combustion of solid municipal waste. This work presents tests of ash from a Polish incineration plant. Nowadays, the management of ash poses a big problem with respect to the high concentration of contaminants that constitutes an environmental nuisance (heavy metals, chlorides, sulfates, etc.). The excessive leaching of contaminants disqualifies ash from being deposited in landfills for hazardous wastes. Bottom ash following the combustion of solid municipal waste mainly contains calcium (23.81%), chlorine (5.44%) and heavy metal (Σ 11.27 g/kg) compounds, while fly ash is characterized by a high content of chlorine (7.22%) and heavy metals (Σ 7.83 g/kg). In the next stage, two concrete mixtures were designed and prepared, containing 30% of ash from combustion of solid municipal waste. The most advantageous physicomechanical properties had concrete mortars that contained 30% of bottom ash: compressive strength—29.48 MPa, bending strength—1678 kN. The performed tests showed that immobilization of dangerous compounds through the C-S-H phase of the concrete significantly decreases the migration of dangerous substance into the environment and minimizes its toxicity. Approximately 97% of the chloride and sulfate salt content was immobilized, and the heavy metal content was immobilized by the C-S-H phase to a degree of 90%. The results obtained provide the option of conveniently managing dangerous wastes with the use of a tight and durable concrete. In many cases, such technology may constitute the best and the cheapest long-term solution in the waste management economy. It may also fill a market gap in this field.