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 ≈0.5 day after the burst, best explained as a jet break with an inferred jet opening angle of ≈4°-8°. 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 ≈(0.6-1.7) × 1051 erg and a circumburst density of ≈5 × 10–3-30 cm–3. From the inferred opening angle of GRB 130603B, we calculate beaming-corrected energies of E γ ≈ (0.5-2) × 1049 erg and E K ≈ (0.1-1.6) × 1049 erg. Along with previous measurements and lower limits we find a median opening angle of ≈10°. Using the all-sky observed rate of 10 Gpc–3 yr–1, this implies a true short GRB rate of ≈20 yr–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 gsim 1 day and conclude that the additional energy component could be due to fall-back accretion or spin-down energy from a magnetar formed following the merger.