Recently, a hybrid analog-digital architecture has been proposed for multiuser MIMO transmission in the millimeter-wave spectrum using reflect-arrays. The architecture exhibits scalability and high energy-efficiency while keeping the transmitter cost-efficient. Inspired by this architecture, we design a secure multiuser hybrid analog-digital precoding scheme. This scheme utilizes the method of regularized least-squares to shape the downlink beamformers, such that the signal received via malicious terminals is effectively suppressed. Numerical investigations depict high robustness of this scheme against the density of malicious terminals, as well as the quality of overhearing channels. Such properties along with high efficiency of the transmitter imply that the proposed scheme is an effective candidate for secure communication in multiuser millimeter-wave massive MIMO systems.