Municipal solid waste incineration (MSWI) fly ash contains high salts and heavy metals, posing challenges for safe disposal and utilization. In this study, cement mortar solidification was applied as a subsequent treatment for washed fly ash. Mortar specimens with 0–62% replacement were prepared, and their phase composition, chemical properties, and heavy metal leaching under simulated acid rain and landfill leachate were analyzed. The results showed that the washing process removed 92.6% of Cl from the raw fly ash, while high concentrations of Pb, Cd, and Cu remained. In mortar, Pb leaching under acid rain increased with fly ash content yet remained below the GB 5085.3 limit. Under landfill leachate, washed fly ash mortar showed reduced Pb, Cd, Ni, and Cu release compared with unwashed ash, though Pb, Cd, and Cu still exceeded GB 16,889 thresholds. Density functional theory calculations demonstrated that Pb2+ can substitute for Ca2+ in the C–S–H lattice, resulting in a 4.2% reduction in unit cell energy and thereby contributing to stable immobilization. These findings provide experimental data and theoretical support for the utilization of washed MSWI fly ash in cement-based materials and for its environmental risk assessment.