This work introduces a novel full-duplex hybrid beamforming (FD-HBF) technique for the millimeter-wave (mmWave) multi-user massive multiple-input multiple-output (MU-mMIMO) systems, where a full-duplex (FD) base station (BS) simultaneously serves half-duplex (HD) downlink and uplink user equipments over the same frequency band. Our main goal is jointly enhancing the downlink/uplink sum-rate capacity via the successful cancellation of the strong self-interference (SI) power. Furthermore, FD-HBF remarkably reduces the hardware cost/complexity in the mMIMO systems by interconnecting the radio frequency (RF) and baseband (BB) stages via a low number of RF chains. First, the RF-stage is constructed via the slow time-varying angular information, where two schemes are proposed for both maximizing the intended signal power and canceling the SI power. Particularly, orthogonal RF beamformer (OBF) scheme only aims canceling the far-field component of SI, while non-orthogonal RF beamformer (NOBF) scheme applies perturbations to the orthogonal beams for also suppressing the near-field component of SI channel. Considering the high computational complexity during the search for optimal perturbations, we apply swarm intelligence to find the optimal perturbations. Second, the BB-stage is designed based on only the reduced-size effective intended channel matrices, where the BB precoder/combiner solutions are obtained via regularized zero-forcing (RZF) and minimum mean square error (MMSE). Hence, the proposed FD-HBF technique does not require the instantaneous SI channel knowledge. It is shown that FD-HBF with NOBF+MMSE achieves 78.1 dB SI cancellation (SIC) on its own. Additionally, FD-HBF with the practical antenna isolation can accomplish more than 130 dB SIC and reduce the SI power below the noise floor. The numerical results present that FD-HBF greatly improves the sum-rate capacity by approximately doubling it compared to its HD counterpart.