In this paper, a novel multi-hop virtual grouping (MHVG) medium access control (MAC) protocol is proposed for ultra dense networks (UDN). The proposed MHVG MAC protocol enables multi-user (MU) downlink (DL) transmission for millimeter wave (mmWave) communications with the goal of enhancing system throughput and mitigating the interference. The proposed MAC permits the scheduling of simultaneous links and the mitigation of the inter- basic service sets (BSS) interference based only on analog beamforming (BF) information, without the necessity for feedback overhead, such as channel state information (CSI). The results of the evaluative simulations conducted demonstrate the superior performance offered by the proposed scheme with respect to average throughput per time slot, signal-to-interference-plus-noise ratio (SINR), and spatial multiplexing gain.