In this study, municipal solid waste incineration (MSWI) fly ash was subjected to mineral carbonation with the aim of investigating CO2 sequestration in waste material. The conducted study follows the trend of searching for alternatives to natural mineral materials with the ability to sequestrate CO2. The mineral carbonation of MSWI fly ash allowed for the storage of up to 0.25 mmol CO2 g−1. Next, both carbonated and uncarbonated MSWI fly ashes were activated using an alkaline activation method by means of two different activation agents, namely potassium hydroxide and potassium silicate or sodium hydroxide and sodium silicate. Mineral carbonation caused a drop in the compressive strength of alkali-activated materials, probably due to the formation of sodium and/or potassium carbonates. The maximum compressive strength obtained was 3.93 MPa after 28 days for uncarbonated fly ash activated using 8 mol dm−3 KOH and potassium hydroxide (ratio 3:1). The relative ratio of hydroxide:silicate also influenced the mechanical properties of the materials. Both carbonated and uncarbonated fly ashes, as well as their alkali-activated derivatives, were characterized in detail by means of XRD, XRF, and FTIR. Both uncarbonated and carbonated fly ashes were subjected to TG analysis. The obtained results have proved the importance of further research in terms of high-calcium fly ash (HCFA) utilization.