Multi-region geocast, an efficient technique for routing protocols at the network layer, realizes the delivery of different information to different user groups that are differentiated from each other by their geographical locations. This paper studies multi-region geocast at the physical layer for the first time by exploiting non- orthogonal multiple access (NOMA) which is one of the promising technologies for future 5G systems. We investigate physical-layer multi-region geocast by studying its beamforming design in a multiple-input single-output (MISO) NOMA system. The objective is to minimize the total transmit power subject to a prescribed data rate for each user group. To this end, we propose an efficient algorithm based on the sequential convex approximation (SCA) method. Our simulation results show that multi-region geocast using NOMA achieves better performance than conventional multi-group multicast when the disparity level among the geographical locations of user groups is remarkable. Further, NOMA is more favorable for limited transmit antennas and massive connectivity in future 5G systems.