Hazardous waste incineration fly ash (HFA) is considered a hazardous waste owing to the high associated concentrations of heavy metals and soluble salts. Hence, cost effective methods are urgently needed to properly dispose HFA. In this study, geopolymers were prepared by alkali-activation technology to stabilize and solidify heavy metals in HFA. In addition, the effects of three different aluminosilicates (metakaolin, fly ash, and glass powder) on the heavy metal immobilization efficiency were investigated. Because the soluble salt content of HFA is too high for their direct placement in flexible landfill sites and water washing can lead to heavy metal leaching, water-washing experiments were conducted after alkali-activation treatment to remove soluble salts. The results suggest that the concentrations of heavy metals leached from geopolymers can satisfy the Chinese Standard limits (GB18598-2019) when the addition of aluminosilicates exceeds 20 wt%. More than 77% of Cl− and >64% of SO42− in geopolymers could be removed via water-washing treatment. The Zn leaching concentration was maintained below approximately 0.52 ppm. After alkali-activation treatment, the water-washing process could efficiently remove soluble salts while inhibiting heavy metal leaching. Sodium-aluminosilicate-hydrate (N-A-S-H) gel, a product of the geopolymerization process in this study, was demonstrated to act as a protective shell that inhibited heavy metal leaching. Hence, HFA-based geopolymers are considered suitable for disposal in flexible landfills.