Molecular-scale components are expected to be central to the realization of nanoscale electronic devices. Although molecular-scale switching has been reported in atomic quantum point contacts, single-molecule junctions provide the additional flexibility of tuning the on/off conductance states through molecular design. To date, switching in single-molecule junctions has been attributed to changes in the conformation or charge state of the molecule. Here, we demonstrate reversible binary switching in a single-molecule junction by mechanical control of the metal-molecule contact geometry. We show that 4,4'-bipyridine-gold single-molecule junctions can be reversibly switched between two conductance states through repeated junction elongation and compression. Using first-principles calculations, we attribute the different measured conductance states to distinct contact geometries at the flexible but stable nitrogen-gold bond: conductance is low when the N-Au bond is perpendicular to the conducting pi-system, and high otherwise. This switching mechanism, inherent to the pyridine-gold link, could form the basis of a new class of mechanically activated single-molecule switches.