We compute the critical Josephson current through a single-molecule junction. As a model for a molecule with a bistable conformational degree of freedom, we study an interacting single-level quantum dot coupled to a two-level system and weakly connected to two superconducting electrodes. We perform a lowest-order perturbative calculation of the critical current and show that it can significantly change due to the two-level system. In particular, the π-junction behavior, generally present for strong interactions, can be completely suppressed. ; Comment: 7 pages, 5 figures; v2: minor changes, to be published in Phys. Rev. B