Context. In recent years, an in-depth γ-ray analysis of the Orion region has been carried out by the AGILE and Fermi/LAT (Large Area Telescope) teams with the aim of estimating the H₂–CO conversion factor, X_CO. The comparison of the data from both satellites with models of diffuse γ-ray Galactic emission unveiled an excess at (l, b)=[213.9, −19.5], in a region at a short angular distance from the OB star κ-Ori. Possible explanations of this excess are scattering of the so-called “dark gas”, non-linearity in the H₂–CO relation, or cosmic-ray (CR) energization at the κ-Ori wind shock. Aims. Concerning this last hypothesis, we want to verify whether cosmic-ray acceleration or re-acceleration could be triggered at the κ-Ori forward shock, which we suppose to be interacting with a star-forming shell detected in several wavebands and probably triggered by high energy particles. Methods. Starting from the AGILE spectrum of the detected γ-ray excess, showed here for the first time, we developed a valid physical model for cosmic-ray energization, taking into account re-acceleration, acceleration, energy losses, and secondary electron contribution. Results. Despite the characteristic low velocity of an OB star forward shock during its “snowplow” expansion phase, we find that the Orion γ-ray excess could be explained by re-acceleration of pre-existing cosmic rays in the interaction between the forward shock of κ-Ori and the CO-detected, star-forming shell swept-up by the star expansion. According to our calculations, a possible contribution from freshly accelerated particles is sub-dominant with respect the re-acceleration contribution. However, a simple adiabatic compression of the shell could also explain the detected γ-ray emission. Futher GeV and TeV observations of this region are highly recommended in order to correctly identify the real physical scenario.