Multicast beamforming utilizes multiple transmit antennas and subscriber channel state information at the transmitter to direct power towards a group of subscribers while limiting interference caused to others. Unfortunately, the natural max-min-fair multicast beamforming formulation is a nonconvex Quadratically Constrained Quadratic Programming (QCQP) problem. This paper proposes a high performance, low complexity Successive Convex Approximation (SCA) algorithm for max-min-fair multicast beamforming with per antenna power constraints in a massive MIMO setting. The proposed approach is based on iterative approximation of the non-convex problem by a sequence of non-smooth, convex optimization problems, and using an inexact version of the Alternating Direction Method of Multipliers for efficiently computing solutions of each SCA subproblem via proximal operator evaluations. Simulations reveal that the algorithm achieves a very favorable performance-complexity tradeoff relative to the existing state-of-the-art.