Since 2016 October, the active galaxy PKS 2247-131 has undergone a γ-ray outburst, which we studied using data obtained with the Fermi Gamma-ray Space Telescope. The emission arises from a relativistic jet in PKS 2247-131, as an optical spectrum only shows a few weak absorption lines, typical of the BL Lacertae sub-class of the blazar class of active galactic nuclei. Here we report a ≃34.5 day quasi-periodic oscillation (QPO) in the emission after the initial flux peak of the outburst. Compared to one-year time-scale QPOs, previously identified in blazars in Fermi energies, PKS 2247-131 exhibits the first clear case of a relatively short, month-like oscillation. We show that this QPO can be explained in terms of a helical structure in the jet, where the viewing angle to the dominant emission region in the jet undergoes periodic changes. The time scale of the QPO suggests the presence of binary supermassive black holes in PKS 2247-131.