The present work explores the effect of a stress relieving heat treatment on the microstructure, tensile properties and residual stresses of the laser powder bed fused AlSi9Cu3 alloy. In fact, the rapid cooling rates together with subsequent heating/cooling cycles occurred during layer by layer additive manufacturing production make low temperature heat treatments desirable for promoting stress relaxation as well as limited grain growth: this combination can offer the opportunity of obtaining the best compromise between high strength, good elongation to failure and limited residual stresses. The microstructural features were analysed, revealing that the high cooling rate, induced by the process, caused a large supersaturation of the aluminum matrix and the refinement of the eutectic structure. Microhardness versus time curve, performed at 250 °C, allowed to identify a stabilization of the mechanical property at a duration of 25 h. The microstructure and the mechanical properties of the samples heat treated at 25 h and at 64 h, considered as a reference for the conventionally produced alloy, were compared with the ones of the as-built alloy. Finally, it was shown that a 59% reduction of the principal residual stresses could be achieved after the 25 h-long treatment and such evolution was correlated to the mechanical behaviour.