The present study was undertaken to understand the effect of annealing on the microstructural features of the melt-pool structure and the associated multiscale mechanical properties of the Al–2.5%Fe–2%Cu alloy manufactured by laser powder bed fusion (LPBF). Microstructural characterizations and tensile tests were conducted for the LPBF-built specimen and those subsequently annealed at various temperatures ranging from 200 to 500 °C. Nanoindentation hardness mapping was used to evaluate the mechanical inhomogeneity of the melt-pool structure and its changes by annealing at different temperatures. The LPBF-manufactured sample exhibited a melt-pool structure containing numerous particles of the Al23CuFe4 phase (oC28, orthorhombic structure) formed because of local melting and rapid solidification during the LPBF process. The relatively coarsened cellular structure localized along the melt-pool boundary resulted in local soft regions. The local vulnerability contributed to the direction dependence of the tensile ductility. A slight variation was observed in the inhomogeneous microstructure of the samples annealed at 200 or 300 °C. The formation of numerous Al23CuFe4 nanoprecipitates in the α-Al supersaturated solid solution prevented strength loss after post-heat treatments. In addition, considerable coarsening of the intermetallic phase after annealing at 500 °C eliminated the melt-pool structure. The tensile performance of the specimens demonstrated a ductile fracture mode, wherein ductile fracture occurred in the α-Al matrix with low hardness while the harder θ-Al13Fe4 stable phase was embedded within it. The anisotropy in the mechanical properties was less pronounced owing to the significant microstructural changes.