Recycling municipal solid waste incineration fly ash (FA) to prepared geopolymer has received wide attentions due to its excellent physical–chemical properties. However, the rich chloride salts and heavy metals in FA limit its FA additive amount during geopolymerization. To address large-scale FA conversion to geopolymer, this work conducted the carbonation pretreatment of FA with H2CO3, (NH4)2CO3 and Na2CO3 (made as H-FA, N-FA and Na-FA, respectively) and further converted it into geopolymers with coal fly ash (CFA). The effect of carbonated FA (50–70 wt.%) on the compressive strength characteristics, efflorescence properties and leaching properties of geopolymer was investigated. The results showed that three types of carbonate solutions changed the mineral phases of FA and consequently affected the properties of geopolymers. The main mineral phases of H-FA and Na-FA were calcite, while calcite and vaterite were the coexisting main mineral phases of N-FA. The prepared geopolymers with Na-FA exhibited the best performance (denser microstructure, better compressive strength, etc.), owing to the formation of more C-S-H and calcite. In particular, the compressive strength of geopolymer with 60 wt.% Na-FA reached the maximum value of 149.89 MPa at curing time for 28 d. Furthermore, the highest leaching concentration of Na in the geopolymers was only 4.52 mg/L, which was at a low level. The leaching concentrations of Pb, Cd, Cr, Cu, Ni and Zn in the geopolymers were far lower than the thresholds of GB 18598–2019. The results confirmed that carbonation pretreatment was a promising approach to improve the recycling of hazardous FA, and converting it to geopolymers with CFA, and FA-based geopolymers had the potential to be applied as building materials.