We report the discovery of a candidate stellar-mass black hole in the Milky Way globular cluster M62. We detected the black hole candidate, which we term M62-VLA1, in the core of the cluster using deep radio continuum imaging from the Karl G. Jansky Very Large Array. M62-VLA1 is a faint source, with a flux density of 18.7 +/- 1.9 microJy at 6.2 GHz and a flat radio spectrum (alpha=-0.24 +/- 0.42, for S_nu = nu^alpha). M62 is the second Milky Way cluster with a candidate stellar-mass black hole; unlike the two candidate black holes previously found in the cluster M22, M62-VLA1 is associated with a Chandra X-ray source, supporting its identification as a black hole X-ray binary. Measurements of its radio and X-ray luminosity, while not simultaneous, place M62-VLA1 squarely on the well-established radio--X-ray correlation for stellar-mass black holes. In archival Hubble Space Telescope imaging, M62-VLA1 is coincident with a star near the lower red giant branch. This possible optical counterpart shows a blue excess, H alpha emission, and optical variability. The radio, X-ray, and optical properties of M62-VLA1 are very similar to those for V404 Cyg, one of the best-studied quiescent stellar-mass black holes. We cannot yet rule out alternative scenarios for the radio source, such as a flaring neutron star or background galaxy; future observations are necessary to determine whether M62-VLA1 is indeed an accreting stellar-mass black hole.