Multi-group multicast beamforming problem with antenna selection is considered in this paper. The rank one constraint which makes the problem nonconvex is embedded into the objective function using exact penalty function. The resulting problem has a bilinear objective function with convex constraints. The equivalent problem is solved iteratively using alternating maximization where a convex optimization problem is solved at each step. Using antenna selection with this effective approach further reduces the total transmitted power significantly compared to the scenario with fixed antennas. The proposed method is computationally efficient and provides significant improvement on reduction of the transmitted power.