This study explores the utilization of municipal solid waste incineration fly ash (MSWIFA) in geopolymer concrete, focusing on compressive strength and heavy metal leachability. MSWIFA was sourced from a Shenzhen waste incineration plant and pretreated by washing to remove soluble salts. Geopolymer concrete was prepared incorporate with washed or unwashed MSWIFA and tested under different pH conditions (2.88, 4.20, and 10.0). Optimal compressive strength was achieved with a Si/Al ratio of 1.5, water/Na ratio of 10, and sand-binder ratio of 0.6. The washing pretreatment significantly enhanced compressive strength, particularly under alkaline conditions, with GP-WFA (washed MSWIFA) exhibiting a 49.6% increase in compressive strength, compared to a 21.3% increase in GP-FA (unwashed MSWIFA). Additionally, GP-WFA’s compressive strength reached 41.7 MPa, comparable to that of the control (GP-control) at 43.7 MPa. Leaching tests showed that acidic conditions (pH 2.88) promoted heavy metal leaching, which increased over the leaching time, while an alkaline environment significantly reduced the leachability of heavy metals. These findings highlight the potential of using washed MSWIFA in geopolymer concrete, promoting sustainable construction practices, particularly in alkaline conditions.