The diffraction from a single periodic metallic grating is shown to be significantly modified when a surface-plasmon polariton wave is excited at the metal-dielectric interface. In particular, vanishing diffraction orders in accordance with scalar diffraction theory, are generated in the presence of the surface wave. This modification is analytically explained, and a plasmonic Bragg law is formulated, which holds both in reflection and in transmission. Furthermore, when the metal layer is sufficiently thin, a dramatic increase in transmission is observed. If the grating is quasiperiodic, new diffraction orders, otherwise nonexisting, are created. We expect this general wave phenomenon to occur whenever a free-space wave is coupled to a surface wave through a periodic structure. Finally, new possibilities of plasmonic Bragg diffraction devices are presented.