The aim of this work is to evaluate the effect of three post-processing heat treatments (HT), from 650 to 1100 °C, on the high-temperature oxidation of laser powder bed fusion (L-PBF) 316L stainless steel. Oxidation tests were conducted at 800 °C for 360 h in a dry air atmosphere and were evaluated by measuring the mass gain. Post-processing HT at 1100 °C of the L-PBF 316L reduced its oxidation resistance at 800 °C because of the grain coarsening and the formation of manganese chromite precipitates, which reduced the content of Cr in the solid solution, hindering the formation of the protective Cr-rich oxide on the surface during the oxidation process. In contrast, HT at 650 and 850 °C slightly increased the oxidation resistance of the alloy because of the formation of a more protective oxide scale during the oxidation process. The results were compared with those of the wrought 316L and showed that L-PBF parts have superior oxidation resistance than wrought ones. In any case, the oxidation behavior of all the tested samples fits a parabolic kinetic law regardless of the processing method. Therefore, in all conditions, a diffusion-controlled oxidation mechanism predominates.