We present radio, optical/NIR, and X-ray observations of the afterglow of the short-duration Swift and Konus-Wind GRB 130603B, and uncover a break in the radio and optical bands at approximately 0.5 day after the burst, best explained as a jet break with an inferred jet opening angle of approximately 4degrees-8degrees. GRB 130603B is only the third short GRB with a radio afterglow detection to date, and represents the first time that a jet break has been evident in the radio band. We model the temporal evolution of the spectral energy distribution to determine the burst explosion properties and find an isotropic-equivalent kinetic energy of approximately (0.6-1.7)x 10 super(51) erg and a circumburst density of approximately 5 x 10 super(-3)-30cm super(-3). From the inferred opening angle of GRB 130603B, we calculate beaming-corrected energies of E sub( gamma ) approximately (0.5-2) x 10 super(49) erg and E sub(K) approximately (0.1-1.6) x 10 super(49) erg. Along with previous measurements and lower limits we find a median opening angle of approximately 10degrees. Using the all-sky observed rate of 10 Gpc super(-3) yr super(-1), this implies a true short GRB rate of approximately 20 yr super(-1) within 200 Mpc, the Advanced LIGO/VIRGO sensitivity range for neutron star binary mergers. Finally, we uncover evidence for significant excess emission in the X-ray afterglow of GRB 130603B at > ~ 1 day and conclude that the additional energy component could be due to fail-back accretion or spin-down energy from a magnetar formed following the merger.