We elucidate in this Letter plasmonic Zener tunneling (PZT) in metal-dielectric waveguide arrays (MDWAs) by using numerical simulations and theoretical analyses. PZT in MDWAs occurs at the waveguide entrance and wherever the beam completes Bloch oscillations, because the bandgap between the first and second bands is minimal at the center of the first Brillouin zone. This feature significantly differs from that of optical Zener tunneling in dielectric waveguide arrays. The dependence of the simulated tunneling rate on the gradient of the relative permittivity of the dielectric layers correlates with the tunneling theory, thus confirming the occurrence of PZT in MDWAs.